Constant density heat exchanger and system for energy conversion

ABSTRACT

A constant density heat exchanger and system for energy conversion is provided. The constant density heat exchanger includes a housing extending between a first end and a second end and defining a chamber having an inlet and an outlet. A first flow control device is positioned at the inlet of the chamber and movable between an open position in which a working fluid is permitted into the chamber and a closed position in which the working fluid is prevented from entering the chamber. A second flow control device is positioned at the outlet of the chamber and movable between an open position in which the working fluid is permitted to exit the chamber and a closed position in which the working fluid is prevented from exiting the chamber. A heat exchange fluid imparts thermal energy to the volume of working fluid as the first flow control device and the second flow control device hold the volume of working fluid at constant density within the chamber.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.16/878,736, filed May 20, 2020, which claims priority to each of thefollowing U.S. Provisional Applications, the contents of which areincorporated herein by reference in their entirety for all purposes asif set forth verbatim: App. No. 62/850,599, filed May 21, 2019; App. No.62/850,623, filed May 21, 2019; App. No. 62/850,678, filed May 21, 2019;App. No. 62/850,692, filed May 21, 2019; and App. No. 62/850,701, filedMay 21, 2019. The present application also incorporates by referenceInternational Patent Application Number PCT/US2020/033674 filed on May20, 2020, in its entirety for all purposes.

FIELD

The present subject matter relates generally to energy conversionsystems, power generation systems, and energy distribution systems. Thepresent subject matter additionally relates to heat exchangers and heatexchanger systems. The present subject matter further relates to pistonengine assemblies, such as closed-cycle engine systems. The presentsubject matter still further relates to systems and methods for controlor operation of one or more systems of the present subject matterherein.

BACKGROUND

Power generation and distribution systems are challenged to provideimproved power generation efficiency and/or lowered emissions.Furthermore, power generation and distribution systems are challenged toprovide improved power output with lower transmission losses. Certainpower generation and distribution systems are further challenged toimprove sizing, portability, or power density generally while improvingpower generation efficiency, power output, and emissions.

Certain engine system arrangements, such as closed cycle engines, mayoffer some improved efficiency over other engine system arrangements.However, closed cycle engine arrangements, such as Stirling engines, arechallenged to provide relatively larger power output or power density,or improved efficiency, relative to other engine arrangements. Closedcycle engines may suffer due to inefficient combustion, inefficient heatexchangers, inefficient mass transfer, heat losses to the environment,non-ideal behavior of the working fluid(s), imperfect seals, friction,pumping losses, and/or other inefficiencies and imperfections. As such,there is a need for improved closed cycle engines and systemarrangements that may provide improved power output, improved powerdensity, or further improved efficiency. Additionally, there is a needfor an improved closed cycle engine that may be provided to improvepower generation and power distribution systems.

Additionally, or alternatively, there is a general need for improvedheat transfer devices, such as for heat engines, or as may be applied topower generation systems, distribution systems, propulsion systems,vehicle systems, or industrial or residential facilities.

Furthermore, there is a need for improved control system and methods foroperating power generation systems as may include subsystems thatcollectively may provide improved power generation efficiency or reducedemissions.

BRIEF DESCRIPTION

Aspects and advantages of the invention will be set forth in part in thefollowing description, or may be obvious from the description, or may belearned through practice of the invention.

An aspect of the present disclosure is directed to a constant densityheat exchanger. The constant density heat exchanger includes a housingextending between a first end and a second end and defining a chamberhaving an inlet and an outlet, a first flow control device positioned atthe inlet of the chamber and movable between an open position in which aworking fluid is permitted into the chamber and a closed position inwhich the working fluid is prevented from entering the chamber, and asecond flow control device positioned at the outlet of the chamber andmovable between an open position in which the working fluid is permittedto exit the chamber and a closed position in which the working fluid isprevented from exiting the chamber. A heat exchange fluid impartsthermal energy to the volume of working fluid as the first flow controldevice and the second flow control device hold the volume of workingfluid at constant density within the chamber.

These and other features, aspects and advantages of the presentinvention will become better understood with reference to the followingdescription and appended claims. The accompanying drawings, which areincorporated in and constitute a part of this specification, illustrateembodiments of the invention and, together with the description, serveto explain the principles of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure including the best mode, directed to oneof ordinary skill in the art, is set forth in the specification, whichmakes reference to the appended figures, in which:

FIG. 1 is a schematic block diagram depicting a system for energyconversion according to an aspect of the present disclosure;

FIG. 2 is a cross sectional view of an exemplary embodiment of a closedcycle engine and load device according to an aspect of the presentdisclosure;

FIG. 3 is a perspective cutaway view of an exemplary portion of anexemplary embodiment of an engine according to an aspect of the presentdisclosure;

FIG. 4 is a side view of an exemplary embodiment of a portion of anengine according to an aspect of the present disclosure;

FIG. 5 is a perspective view of an exemplary embodiment of a portion ofan engine such as provided in regard to FIG. 4;

FIG. 6 is another perspective view of an exemplary embodiment of aportion of an engine such as provided in regard to FIGS. 4 through FIG.5;

FIG. 7 is an end view of an exemplary embodiment of a portion of anengine such as provided in regard to FIGS. 4 through FIG. 5;

FIG. 8 provides a schematic view of a Notarnicola cycle system operableto produce useful work according to an example embodiment of the presentdisclosure;

FIGS. 9 and 10 provide schematic close-up views of one embodiment of aconstant density heat exchanger that can be utilized in the system ofFIG. 8;

FIG. 11 provides a schematic view of another system operable to produceuseful work according to an example embodiment of the presentdisclosure;

FIG. 12 graphically depicts the mass flow rate of the working fluid atthe outlet of the constant density heat exchanger as a function of time;

FIGS. 13 and 14 provide cross-sectional views of example pulseconverters that can be utilized with Notarnicola cycle systems of thepresent disclosure;

FIG. 15 provides a schematic view of yet another system operable toproduce useful work according to an example embodiment of the presentdisclosure;

FIG. 16 provides a schematic view of a power generation system accordingto an example embodiment of the present disclosure;

FIG. 17 provides a schematic view of a power generation system accordingto an example embodiment of the present disclosure;

FIG. 18 provides a close-up schematic view of the bottoming-cycle systemof the power generation system of FIG. 17;

FIG. 19 graphically depicts the advantages of the constant density heatapplication process of a Notarnicola cycle system;

FIG. 20 provides a schematic view of another power generation systemb100 according to an example embodiment of the present disclosure;

FIG. 21 provides a schematic view of another power generation systemb100 according to an example embodiment of the present disclosure;

FIG. 22 provides a schematic view of a power generation system b100according to an example embodiment of the present disclosure;

FIG. 23 provides a schematic view of another Notarnicola cycle systemoperable to produce useful work according to an example embodiment ofthe present disclosure;

FIG. 24 provides a schematic view of another Notarnicola cycle systemoperable to produce useful work according to an example embodiment ofthe present disclosure;

FIG. 25 provides a schematic cross-sectional view of an example linearconstant density heat exchanger according to an aspect of the presentdisclosure;

FIG. 26 provides a schematic cross sectional view of another linearconstant density heat exchanger according to an example embodiment ofthe present disclosure;

FIG. 27 provides a side view of a housing that can be implemented in alinear constant density heat exchanger according to an exampleembodiment of the present disclosure;

FIG. 28 provides a close-up view of a second end of the housing of FIG.27 and depicts a plurality of heat exchange tubes with their ends cutofffor illustrative purposes;

FIG. 29 provides a schematic cross sectional view of another examplelinear constant density heat exchanger according to an aspect of thepresent disclosure;

FIG. 30 provides a flow diagram for a method of controlling a linearconstant density heat exchanger according to an aspect of the presentdisclosure;

FIG. 31 provides a perspective view of a rotary constant density heatexchanger according to an example embodiment of the present disclosure;

FIG. 32 provides a front view of the rotary constant density heatexchanger of FIG. 31;

FIG. 33 provides a cross-sectional view of the rotary constant densityheat exchanger of FIGS. 31 and 32 with the ports of the first plate andsecond plate positioned at a twelve o'clock position;

FIG. 34 provides a cross-sectional view of the rotary constant densityheat exchanger of FIGS. 31 and 32 with the ports of the first plate andsecond plate not positioned at the twelve o'clock position;

FIG. 35 provides a cross-sectional view of the rotary constant densityheat exchanger of FIGS. 31 and 32 with the ports of the first plate andsecond plate positioned at the twelve o'clock position after onerevolution of the plates;

FIG. 36 provides a cross-sectional view of another rotary constantdensity heat exchanger having one or more heat sources positionedradially inward of the working chambers;

FIG. 37 provides a front view of another rotary constant density heatexchanger according to an example embodiment of the present disclosure;

FIGS. 38 and 39 provide front views of another rotary constant densityheat exchanger according to an example embodiment of the presentdisclosure;

FIGS. 40, 41, and 42 provide various views of another rotary constantdensity heat exchanger according to an example embodiment of the presentdisclosure;

FIG. 43 provides a schematic view of another rotary constant densityheat exchanger according to an example embodiment of the presentdisclosure;

FIGS. 44, 45, 46, and 47 provide various views of an example Wrankeldevice and components thereof according to an aspect of the presentdisclosure;

FIGS. 48 through 53 provide various schematic axial views of the Wrankeldevice of FIGS. 44 through 47 and show the rotor in different positionsthrough its rotation or eccentric path; and

FIG. 54 provides a schematic axial view of another Wrankel deviceaccording to an example embodiment of the present disclosure; and

FIG. 55 provides an exemplary computing system according to aspects ofthe present disclosure.

Repeat use of reference characters in the present specification anddrawings is intended to represent the same or analogous features orelements of the present disclosure.

DETAILED DESCRIPTION

Reference now will be made in detail to embodiments of the disclosure,one or more examples of which are illustrated in the drawings. Eachexample is provided by way of explanation of the disclosure and notlimitation. In fact, it will be apparent to those skilled in the artthat various modifications and variations can be made in the presentdisclosure without departing from the scope of the disclosure. Forinstance, features illustrated or described as part of one embodimentcan be used with another embodiment to yield a still further embodiment.In another instance, ranges, ratios, or limits associated herein may bealtered to provide further embodiments, and all such embodiments arewithin the scope of the present disclosure. Unless otherwise specified,in various embodiments in which a unit is provided relative to a ratio,range, or limit, units may be altered, and/or subsequently, ranges,ratios, or limits associated thereto are within the scope of the presentdisclosure. Thus, it is intended that the present disclosure covers suchmodifications and variations as come within the scope of the appendedclaims and their equivalents.

As used herein, the terms “first”, “second”, and “third” may be usedinterchangeably to distinguish one component from another and are notintended to signify location or importance of the individual components.

The terms “upstream” and “downstream” refer to the relative directionwith respect to fluid flow in a fluid pathway. For example, “upstream”refers to the direction from which the fluid flows, and “downstream”refers to the direction to which the fluid flows. The term “loop” can beany suitable fluid pathway along which fluid can flow and can be eitheropen or closed, unless stated otherwise.

Generally, current power generation and distribution systems areinflexible (e.g., due to cost and operational needs and restrictions)relative to changes in usage and demand throughout a day. Additionally,such inflexibility may be exasperated by periodic, irregular, orunpredictable power generation from renewable energy sources.

In addition, or alternatively, power generation and distributioninfrastructure is costly and renders large geographic areas vulnerableto power outages based on adverse weather, natural or man-madedisasters, equipment malfunctions and failures, or maintenanceactivities. Initial and on-going costs, such as maintenance and repair,result in barriers to further development of access to electricity indeveloping countries and rural areas. Expanding access to electricitymay be hindered by relatively high costs to establish generation anddistribution infrastructure, relatively high operational costs, and anability for governments, corporations, or consumers to pay or invest inpower generation and distribution. Such costs may also pose barriers tofurther maintenance and development in developed countries, as olderinfrastructure and natural or man-made disasters may cause maintenanceor improvement to be cost-prohibitive. For example, in the UnitedStates, power lines and transformers are approximately 30 years old onaverage. Replacement costs for such equipment have been estimated atover $1 trillion dollars.

Such issues and barriers from power generation and distribution systemsmay further pose barriers to developing or expanding access to cleanwater, water desalination, and food security. Additionally, oralternatively, smaller scale or portable power generation systems thatmay overcome distribution obstacles may nonetheless be challenged toprovide a necessary power density and output. Such limitations in powerdensity and output may generally result in an inability to apply smallerscale or portable power generation systems to rural areas or developingnations. Furthermore, as clean water treatment and desalination aregenerally energy intensive, smaller scale or portable power generationsystem may generally provide inadequate power density and output forproviding water to rural or less population-dense areas.

As such, there is a need for power generation systems that provideimproved efficiency and reduced emissions over known power generationsystems that may further be sized or scaled to provide improved powerdistribution without adversely affecting efficiency and emissions. Theneed for improved power generation systems is further, or alternatively,such that issues regarding power distribution, power generation versuschanging peak power demands, emissions, barriers to infrastructuredevelopment, and challenges and limitations posed by vehicleelectrification may each be addressed, improved upon, or alleviated.

Small-scale or portable power generation systems are desirable forapplications including space vehicles and systems, automotive drivetrainand aerospace propulsion electrification, direct cooling sources, andportable or distributed power generation such as to address issuesregarding power generation efficiency, density, and output. However,there is a need for improved thermal efficiency, electrical conversionefficiency, or both, for such systems.

System for Energy Conversion

Referring now to FIG. 1, an exemplary schematic block diagram depictinga system for energy conversion (hereinafter, “system A10”) is provided.Various embodiments of the system A10 provided herein include systemsfor power generation, a heat recovery system, a heat pump or cryogeniccooler, a system including and/or acting as a bottoming cycle and/or atopping cycle, or other system for producing useful work or energy, orcombinations thereof. Referring additionally for FIG. 2, variousembodiments of the system A10 include a closed cycle engine apparatus(hereinafter, “engine A100”, apparatus “A100”, or “engine assemblyC900”, or otherwise denoted herein) operably coupled to a load devicec092. The engine A100 contains a substantially fixed mass of an engineworking fluid to which and from which thermal energy is exchanged at arespective cold side heat exchanger A42 and a hot side heat exchangerC108. In one embodiment, the engine working fluid is helium. In otherembodiments, the engine working fluid may include air, nitrogen,hydrogen, helium, or any appropriate compressible fluid, or combinationsthereof. In still various embodiments, any suitable engine working fluidmay be utilized in accordance with the present disclosure. In exemplaryembodiments, the engine working fluid may include a gas, such as aninert gas. For example, a noble gas, such as helium may be utilized asthe engine working fluid. Exemplary working fluids preferably are inert,such that they generally do not participate in chemical reactions suchas oxidation within the environment of the engine. Exemplary noblegasses include monoatomic gases such as helium, neon, argon, krypton, orxenon, as well as combinations of these. In some embodiments, the engineworking fluid may include air, oxygen, nitrogen, or carbon dioxide, aswell as combinations of these. In still various embodiments, the engineworking fluid may be liquid fluids of one or more elements describedherein, or combinations thereof. It should further be appreciated thatvarious embodiments of the engine working fluid may include particles orother substances as appropriate for the engine working fluid.

In various embodiments, the load device C092 is a mechanical work deviceor an electric machine. In one embodiment, the load device C092 is apump, compressor, or other work device. In another embodiment, the loaddevice C092 as an electric machine is configured as a generatorproducing electric energy from movement of a piston assembly A1010 atthe engine. In still another embodiment, the electric machine isconfigured as a motor providing motive force to move or actuate thepiston assembly A1010, such as to provide initial movement (e.g., astarter motor). In still various embodiments, the electric machinedefines a motor and generator or other electric machine apparatus suchas described further herein.

A heater body C100 is thermally coupled to the engine A100. The heaterbody C100 may generally define any apparatus for producing or otherwiseproviding a heating working fluid such as to provide thermal energy tothe engine working fluid. Various embodiments of the heater body C100are further provided herein. Exemplary heater bodies C100 may include,but are not limited to, a combustion or detonation assembly, an electricheater, a nuclear energy source, a renewable energy source such as solarpower, a fuel cell, a heat recovery system, or as a bottoming cycle toanother system. Exemplary heater bodies C100 at which a heat recoverysystem may be defined include, but are not limited to, industrial wasteheat generally, gas or steam turbine waste heat, nuclear waste heat,geothermal energy, decomposition of agricultural or animal waste, moltenearth or metal or steel mill gases, industrial drying systems generallyor kilns, or fuel cells. The exemplary heater body C100 providingthermal energy to the engine working fluid may include all or part of acombined heat and power cycle, or cogeneration system, or powergeneration system generally.

In still various embodiments, the heater body C100 is configured toprovide thermal energy to the engine working fluid via a heating workingfluid. The heating working fluid may be based, at least in part, on heatand liquid, gaseous, or other fluid provided by one or more fuel sourcesand oxidizer sources providing a fuel and oxidizer. In variousembodiments, the fuel includes, but is not limited to, hydrocarbons andhydrocarbon mixtures generally, “wet” gases including a portion ofliquid (e.g., humid gas saturated with liquid vapor, multiphase flowwith approximately 10% liquid and approximately 90% gas, natural gasmixed with oil, or other liquid and gas combinations, etc.), petroleumor oil (e.g., Arabian Extra Light Crude Oil, Arabian Super Light, LightCrude Oil, Medium Crude Oil, Heavy Crude Oil, Heavy Fuel Oil, etc.),natural gas (e.g., including sour gas), biodiesel condensate or naturalgas liquids (e.g., including liquid natural gas (LNG)), dimethyl ether(DME), distillate oil #2 (DO2), ethane (C₂), methane, high H₂ fuels,fuels including hydrogen blends (e.g., propane, butane, liquefiedpetroleum gas, naphtha, etc.), diesel, kerosene (e.g., jet fuel, suchas, but not limited to, Jet A, Jet A-1, JP1, etc.), alcohols (e.g.,methanol, ethanol, etc.), synthesis gas, coke over gas, landfill gases,etc., or combinations thereof.

In various embodiments, the system A10 includes a working fluid bodyC108, such as further described herein. In one embodiment, the workingfluid body C108 defines a hot side heat exchanger A160, such as furtherdescribed herein, from which thermal energy is output to the engineworking fluid at an expansion chamber A221 of the engine. The workingfluid body C108 is positioned at the expansion chamber A221 of theengine in thermal communication with the heater body C100. In otherembodiments, the working fluid body C108 may be separate from the heaterbody C100, such that the heating working fluid is provided in thermalcommunication, or additionally, in fluid communication with the workingfluid body C108. In particular embodiments, the working fluid body C108is positioned in direct thermal communication with the heater body C100and the expansion chamber A221 of the engine A100 such as to receivethermal energy from the heater body C100 and provide thermal energy tothe engine working fluid within the engine.

In still various embodiments, the heater body C100 may include a singlethermal energy output source to a single expansion chamber A221 of theengine. As such, the system A10 may include a plurality of heaterassemblies each providing thermal energy to the engine working fluid ateach expansion chamber A221. In other embodiments, such as depicted inregard to FIG. 2, the heater body C100 may provide thermal energy to aplurality of expansion chambers A221 of the engine. In still otherembodiments, such as depicted in regard to FIG. 8, the heater bodyincludes a single thermal energy output source to all expansion chambersA221 of the engine.

The system A10 further includes a chiller assembly, such as chillerassembly A40 further described herein. The chiller assembly A40 isconfigured to receive and displace thermal energy from a compressionchamber A222 of the engine. The system A10 includes a cold side heatexchanger A42 thermally coupled to the compression chamber A222 of theclosed cycle engine and the chiller assembly. In one embodiment, thecold side heat exchanger A42 and the piston body C700 defining thecompression chamber A222 of the engine are together defined as anintegral, unitary structure. In still various embodiments, the cold sideheat exchanger A42, at least a portion of the piston body C700 definingthe compression chamber A222, and at least a portion of the chillerassembly together define an integral, unitary structure.

In various embodiments, the chiller assembly A40 is a bottoming cycle tothe engine A100. As such, the chiller assembly A40 is configured toreceive thermal energy from the engine A100. The thermal energy receivedat the chiller assembly A40, such as through a cold side heat exchangerA42, or cold side heat exchanger A170 further herein, from the engineA100 is added to a chiller working fluid at the chiller assembly A40. Invarious embodiments, the chiller assembly A40 defines a Rankine cyclesystem through which the chiller working fluid flows in closed looparrangement with a compressor. In some embodiments, the chiller workingfluid is further in closed loop arrangement with an expander. In stillvarious embodiments, the system A10 includes a heat exchanger A88 (FIG.3). In various embodiments, the heat exchanger A188 may include acondenser or radiator. The cold side heat exchanger A40 is positioneddownstream of the compressor and upstream of the expander and in thermalcommunication with a compression chamber A222 of the closed cycleengine, such as further depicted and described in regard to FIG. 2-FIG.3. In various embodiments, the cold side heat exchanger A42 maygenerally define an evaporator receiving thermal energy from the engineA40.

Referring still to FIG. 1, in some embodiments, the heat exchanger A188is positioned downstream of the expander and upstream of the compressorand in thermal communication with a cooling working fluid. In theschematic block diagram provided in FIG. 1, the cooling working fluid isan air source. However, in various embodiments, the cooling fluid maydefine any suitable fluid in thermal communication with the heatexchanger. The heat exchanger may further define a radiator configuredto emit or dispense thermal energy from the chiller assembly A40. A flowof cooling working fluid from a cooling fluid source is provided inthermal communication with the heat exchanger to further aid heattransfer from the chiller working fluid within the chiller assembly A40to the cooling working fluid.

As further described herein, in various embodiments the chiller assemblyA40 may include a substantially constant density heat exchanger. Theconstant density heat exchanger generally includes a chamber includingan inlet and an outlet each configured to contain or trap a portion ofthe chiller working fluid for a period of time as heat from the closedcycle engine is transferred to the cold side heat exchanger A42. Invarious embodiments, the chamber may define a linear or rotary chamberat which the inlet and the outlet are periodically opened and closed viavalves or ports such as to trap the chiller working fluid within thechamber for the desired amount of time. In still various embodiments,the rate at which the inlet and the outlet of the chamber defining theconstant density heat exchanger is a function at least of velocity of aparticle of fluid trapped within the chamber between the inlet and theoutlet. The chiller assembly A40 including the constant density heatexchanger may provide efficiencies, or efficiency increases,performances, power densities, etc. at the system A10 such as furtherdescribed herein.

It should be appreciated that in other embodiments, the chiller assemblyA40 of the system A10 may include a thermal energy sink generally. Forexample, the chiller assembly A40 may include a body of water, thevacuum of space, ambient air, liquid metal, inert gas, etc. In stillvarious embodiments, the chiller working fluid at the chiller assemblyA40 may include, but is not limited to, compressed air, water orwater-based solutions, oil or oil-based solutions, or refrigerants,including, but not limited to, class 1, class 2, or class 3refrigerants. Further exemplary refrigerants may include, but are notlimited to, a supercritical fluid including, but not limited to, carbondioxide, water, methane, ethane, propane, ethylene, propylene, methanol,ethanol, acetone, or nitrous oxide, or combinations thereof. Stillexemplary refrigerants may include, but are not limited to, halon,perchloroolefin, perchlorocarbon, perfluoroolefin, perfluororcarbon,hydroolefin, hydrocarbon, hydrochloroolefin, hydrochlorocarbon,hydrofluoroolefin, hydrofluorocarbon, hydrochloroolefin,hydrochlorofluorocarbon, chlorofluoroolefin, or chlorofluorocarbon typerefrigerants, or combinations thereof. Still further exemplaryembodiments of refrigerant may include, but are not limited to,methylamine, ethylamine, hydrogen, helium, ammonia, water, neon,nitrogen, air, oxygen, argon, sulfur dioxide, carbon dioxide, nitrousoxide, or krypton, or combinations thereof.

It should be appreciated that where combustible or flammablerefrigerants are included for the chiller working fluid, variousembodiments of the system A10 may beneficially couple the heater bodyC100, and/or the fuel source, and the chiller assembly A40 in fluidcommunication such that the combustible or flammable working fluid towhich thermal energy is provided at the chiller assembly A40 may furtherbe utilized as the fuel source for generating heating working fluid, andthe thermal energy therewith, to output from the heater body C100 to theengine working fluid at the engine A100.

Various embodiments of the system A10 include control systems andmethods of controlling various sub-systems disclosed herein, such as,but not limited to, the fuel source, the oxidizer source, the coolingfluid source, the heater body C100, the chiller assembly C40, the engineA100, and the load device C092, including any flow rates, pressures,temperatures, loads, discharges, frequencies, amplitudes, or othersuitable control properties associated with the system A10. In oneaspect, a control system for the system A10 defining a power generationsystem is provided. The power generation system includes one or moreclosed cycle engines (such as engine A100), one or more load devicesdefining electric machines (such as load device C092) operativelycoupled to the engine, and one or more energy storage devices incommunication with the electric machines.

The control system can control the closed cycle engine and itsassociated balance of plant to generate a temperature differential, suchas a temperature differential at the engine working fluid relative tothe heating working fluid and the chiller working fluid. Thus, theengine defines a hot side, such as at the expansion chamber A221, and acold side, such as at the compression chamber A222. The temperaturedifferential causes free piston assemblies A1010 to move within theirrespective piston chambers defined at respective piston bodies C700. Themovement of the pistons A1011 causes the electric machines to generateelectrical power. The generated electrical power can be provided to theenergy storage devices for charging thereof. The control system monitorsone or more operating parameters associated with the closed cycleengine, such as piston movement (e.g., amplitude and position), as wellas one or more operating parameters associated with the electricmachine, such as voltage or electric current. Based on such parameters,the control system generates control commands that are provided to oneor more controllable devices of the system A10. The controllable devicesexecute control actions in accordance with the control commands.Accordingly, the desired output of the system A10 can be achieved.

Furthermore, the control system can monitor and anticipate load changeson the electric machines and can control the engine A100 to anticipatesuch load changes to better maintain steady state operation despitedynamic and sometimes significant electrical load changes on theelectric machines. A method of controlling the power generation systemis also provided. In another aspect, a control system for a heat pumpsystem is provided. The heat pump system includes one or more of theclosed cycle engines described herein. A method of controlling the heatpump system is also provided. The power generation and heat pump systemsas well as control methods therefore are provided in detail herein.

Energy Conversion Apparatus

Referring now to FIG. 2-FIG. 3, exemplary embodiments of the system A10are further provided. FIG. 2 is an exemplary cross sectional view of thesystem A10 including the heater body C100 and the chiller assembly A40each in thermal communication with the engine A100, or particularly theengine working fluid within the engine A100, such as shown and describedaccording to the schematic block diagram of FIG. 1. FIG. 3 is anexemplary cutaway perspective view of a portion of the engine A100. Thesystem A10 includes a closed cycle engine A100 including a pistonassembly A1010 positioned within a volume or piston chamber defined by awall defining a piston body C700. The volume within the piston body C700is separated into a first chamber, or hot chamber, or expansion chamberA221 and a second chamber, or cold chamber (relative to the hotchamber), or compression chamber A222 by a piston A1011 of the pistonassembly A1010. The expansion chamber A221 is positioned thermallyproximal to the heater body C100 relative to the compression chamberA222 thermally distal to the heater body C100. The compression chamberA222 is positioned thermally proximal to the chiller assembly A40relative to the expansion chamber A221 thermally distal to the chillerassembly A40.

In various embodiments, the piston assembly A1010 defines a double-endedpiston assembly A1010 in which a pair of pistons A1011 is each coupledto a connection member A1030. The connection member A1030 may generallydefine a rigid shaft or rod extended along a direction of motion of thepiston assembly A1010. In other embodiments, the connection membersA1030 includes one or more springs or spring assemblies, such as furtherprovided herein, providing flexible or non-rigid movement of theconnection member A1030. In still other embodiments, the connectionmember A1030 may further define substantially U- or V-connectionsbetween the pair of pistons A1011.

Each piston A1011 is positioned within the piston body C700 such as todefine the expansion chamber A221 and the compression chamber A222within the volume of the piston body C700. The load device c092 isoperably coupled to the piston assembly A1010 such as to extract energytherefrom, provide energy thereto, or both. The load device c092defining an electric machine is in magnetic communication with theclosed cycle engine via the connection member A1030. In variousembodiments, the piston assembly A1010 includes a dynamic member A181positioned in operable communication with a stator assembly A182 of theelectric machine. The stator assembly A182 may generally include aplurality of windings wrapped circumferentially relative to the pistonassembly A1010 and extended along a lateral direction L. In oneembodiment, such as depicted in regard to FIG. 2, the dynamic memberA181 is connected to the connection member A1030. The electric machinemay further be positioned between the pair of pistons A1011 of eachpiston assembly A1010. Dynamic motion of the piston assembly A1010generates electricity at the electric machine. For example, linearmotion of the dynamic member A181 between each pair of chambers definedby each piston A1011 of the piston assembly A1010 generates electricityvia the magnetic communication with the stator assembly A182 surroundingthe dynamic member A181.

Referring to FIG. 2-FIG. 3, in various embodiments, the working fluidbody C108 may further define at least a portion of the expansion chamberA221. In one embodiment, such as further described herein, the workingfluid body C108 defines a unitary or monolithic structure with at leasta portion of the piston body C700, such as to define at least a portionof the expansion chamber A221. In some embodiments, the heater body C100further defines at least a portion of the working fluid body C108, suchas to define a unitary or monolithic structure with the working fluidbody C108, such as further described herein. In one embodiment, thesystem A10 includes the hot side heat exchanger or working fluid bodyC108 positioned between the heater body C100 and the expansion chamberA221 of the piston body C700. In various embodiments, the working fluidbody C108 includes a plurality of heater conduits or working fluidpathways C110 extended from the expansion chamber A221.

The engine A100 defines an outer end A103 and an inner end A104 eachrelative to a lateral direction L. The outer ends A103 define laterallydistal ends of the engine A100 and the inner ends 104 define laterallyinward or central positions of the engine A100. In one embodiment, suchas depicted in regard to FIG. 2-FIG. 3, the heater body C100 ispositioned at outer ends A103 of the system A10. The piston body C700includes a dome structure A26 at the expansion chamber A221. Theexpansion chamber dome structure A26 s provides reduced surface areaheat losses across the outer end A103 of the expansion chamber A221. Invarious embodiments, the pistons A1011 of the piston assembly A1010further include domed pistons A1011 corresponding to the expansionchamber A221 dome. The dome structure A26, the domed piston A1011, orboth may provide higher compressions ratios at the chambers A221, A222,such as to improve power density and output.

The chiller assembly A40 is positioned in thermal communication witheach compression chamber A222. Referring to FIG. 2-FIG. 3, the chillerassembly A40 is positioned inward along the lateral direction L relativeto the heater body C100. In one embodiment, the chiller assembly A40 ispositioned laterally between the heater body C100 and the load devicec092 along the lateral direction L. The chiller assembly A40 providesthe chiller working fluid in thermal communication with the engineworking fluid at the cold side heat exchanger A42 and/or compressionchamber A222. In various embodiments, the piston body C700 defines thecold side heat exchanger A42 between an inner volume wall A46 and anouter volume wall A48 surrounding at least the compression chamber A222portion of the piston body C700.

In various embodiments, such as depicted in regard to FIG. 2-FIG. 3, theload device c092 is positioned at the inner end A104 of the system A10between laterally opposing pistons A1011. The load device c092 mayfurther include a machine body c918 positioned laterally between thepiston bodies C700. The machine body c918 surrounds and houses thestator assembly A182 of the load device c092 defining the electricmachine. The machine body c918 further surrounds the dynamic member A181of the electric machine attached to the connection member A1030 of thepiston assembly A1010. In various embodiments, such as depicted inregard to FIG. 2-FIG. 3, the machine body c918 further provides an innerend wall A50 at the compression chamber A222 laterally distal relativeto the expansion chamber A221 dome.

In various embodiments, the compression chamber A222 of one pistonassembly A1010 is fluidly connected to the expansion chamber A221 ofanother piston assembly A1010 via the walled conduit A1050 to provide abalanced pressure and/or balanced phase fluid coupling arrangement ofthe plurality of chambers A221, A222. An interconnected volume ofchambers including the expansion chamber A221 of one piston assemblyA1010 and the compression chamber A222 of another piston assembly A1010defines a fluid interconnection of the chambers A221, A222 at differentpiston assemblies A1010. The fluid interconnection of chambers A221,A222 at different piston assemblies is such that if there is any fluidcommunication or fluid leakage path between the expansion chamber A221and the compression chamber A222 of the same piston assembly A1010, asingle fluid loop of connected chambers A221, A222 is provided that isseparated from the chambers A221, A222 outside of the interconnectedvolume of chambers. In one embodiment, the balanced pressurearrangement, or additionally, the balance phase arrangement, of thepiston assemblies A1010 is the fluid interconnection of the walledconduits A1050 and the chambers A221, A222 such that the chambers withinthe interconnected volume are substantially fluidly and/or pneumaticallyseparated from those outside of the interconnected volume to provide asubstantially equal and opposite force relative to one another to atleast one piston assembly A1010 when the engine working fluid within thechambers A221, A222 is at a uniform temperature. Stated differently,when one piston assembly A1010 is articulated, such as along the lateraldirection L, the fluid interconnection of chambers A221, A222 via thewalled conduit A1050 provides a substantially net zero force at anotherpiston assembly A1010 when the engine working fluid is at asubstantially uniform temperature. As such, when one piston assemblyA1010 is articulated under such conditions, adjacent or other pistonassemblies A1010 remain stationary due at least to the net zero force atthe piston assembly A1010. In various embodiments, the substantiallyuniform temperature is defined when no heat input or thermal energy isprovided from the heater body C100 or working fluids body C108 to theengine working fluid.

Engine Chamber to Chamber Conduits Arrangements

The cross sectional view provided in FIG. 2 is cut along the lateraldirection L such as to depict two of four piston assemblies A1010 of thesystem A10. In various embodiments, the system A10 provided in regard toFIG. 2 further includes the walled conduits A1050 disposed inward of thepiston bodies C700 proximate to the reference longitudinal axis C204. Inother embodiments, the system A10 provided in regard to FIG. 2 furtherincludes the walled conduits A1050 disposed outward of the piston bodiesC700, such as shown and described in regard to FIG. 4 through FIG. 7.

Referring to FIG. 4 through FIG. 7, side, end, and perspective views ofa portion of the system A10 are provided. The embodiments provided inregard to FIG. 4 through FIG. 7 are configured substantially similarlyas shown and described in regard to FIG. 2-FIG. 3. In regard to FIGS.4-FIG. 7, the portions of the system A10 depicted therein include fourpiston assemblies A1010 positioned within eight respective piston bodiesC700. The piston bodies C700 may generally include the first volume walland the second volume wall shown and described in regard to FIG. 2-FIG.3. The piston bodies C700 may generally define cylinders into whichpistons A1011 of the piston assembly A1010 are each positioned such asto define the expansion chamber A221 and the compression chamber A222within each piston body C700. However, it should be appreciated thatother suitable geometries of the piston body C700 containing the pistonA1011 may be utilized.

The engine A100 further includes a plurality of walled conduits A1050connecting particular chambers A221, A222 of each piston body C700 (FIG.2) such as to define a balanced pressure arrangement of the pistonsA1011. In various embodiments, the engine A100 includes at least oneinterconnected volume of chambers A221, A222 such as described herein.In one embodiment, such as depicted in regard to FIGS. 4-FIG. 7, theengine A100 includes two interconnected volumes in which eachinterconnected volume includes an expansion chamber A221 of a firstpiston body C700 of a first piston assembly A1010 connected in fluidcommunication of the engine working fluid with a compression chamberA222 of a second piston body C700 of a second piston assembly A1010 eachconnected by a conduit A1050. More particularly, the balanced pressurearrangement of piston assemblies A1010 depicted in regard to FIGS.4-FIG. 7 includes two interconnected volumes each substantially fluidlyseparated from one another and/or substantially pneumatically separatedfrom one another. The fluidly separated and/or pneumatically separatedarrangement of chambers A221, A222 into the interconnected volume, andthose chambers A221, A222 outside of the interconnected volume or inanother interconnected volume, is particularly provided via thearrangement of expansion chambers A221 connected to compression chambersA222 via the walled conduits A1050 such as further described herein.

In various embodiments, the interconnected volume includes pairs of theexpansion chamber A221 fluidly coupled to the compression chamber A222each defined at laterally separated ends of the piston assemblies A1010.In one embodiment, the engine A100 defines a first end 101 separatedalong the lateral direction L by the connection member A1030 from asecond end 102, such as depicted in FIG. 5 and FIG. 6. Each end of theengine A100 defines an expansion chamber A221 and a compression chamberA222 at each piston A1011 of each piston assembly A1010. The engine A100depicted in FIGS. 4-FIG. 7, and further in regard to FIG. 2, includesthe expansion chamber A221 at one end connected to a respectivecompression chamber A222 at another end via respective conduits. In oneembodiment, such as depicted in FIGS. 5 and 6, the engine A100 includestwo expansion chambers A221 at the first end 101 each connected torespective compression chambers A222 at the second end 102 viarespective conduits A1050. The engine A100 further includes twoexpansion chambers A221 at the second end 102 each connected torespective compression chamber A222 at the first end 101 via respectiveconduits A1050. The system A10 further includes four expansion chambersA221 at one end each connected to respective compression chambers A222at the same end via respective conduits A1050. In one embodiment, thesystem A10 includes two expansion chambers A221 at the first end 101each connected to respective compression chambers A222 at the first end101 via respective walled conduits A1050. The system A10 furtherincludes two expansion chambers A221 at the second end 102 eachconnected to respective compression chambers A222 at the second end 102via respective walled conduits A1050.

In one embodiment, the engine includes four piston assemblies A1010extended along the lateral direction L and in circumferentialarrangement relative to the reference longitudinal axis C204. The pistonassemblies A1010 may be positioned equidistant to one another around thereference longitudinal axis C204. In one embodiment, a pair of theheater body is positioned at outer ends A103 of the engine. The heaterbody is positioned proximate to the expansion chamber A221 and distal tothe compression chamber A222. Each heater body may be positioned andconfigured to provide a substantially even flow of thermal energy tofour hot side heat exchangers 160 or expansion chambers A221 at a time.

In general, the exemplary embodiments of system A10 and engine, orportions thereof, described herein may be manufactured or formed usingany suitable process. However, in accordance with several aspects of thepresent subject matter, some or all of system A10 may be formed using anadditive manufacturing process, such as a 3-D printing process. The useof such a process may allow portions of the system A10 to be formedintegrally, as a single monolithic component, or as any suitable numberof sub-components. In various embodiments, the manufacturing process mayallow the all or part of the heater body, the chiller assembly, the loaddevice c092, or the engine to be integrally formed and include a varietyof features not possible when using prior manufacturing methods. Forexample, the additive manufacturing methods described herein provide themanufacture of the system A10 having unique features, configurations,thicknesses, materials, densities, and structures not possible usingprior manufacturing methods. Some of these novel features can, forexample, improve thermal energy transfer between two or more components,improve thermal energy transfer to the engine working fluid, improvethermal energy transfer from the engine working fluid to the chillerworking fluid, reduce leakages, or facilitate assembly, or generallyimprove thermal efficiency, power generation and output, or powerdensity of the system A10 using an additive manufacturing process asdescribed herein.

Balance of Plant

In one aspect, example embodiments of a balance of plant for a primepower generator are provided. A balance of plant for a power generationsystem can be described as the supporting components and systems of theprime power generator of the system. In some embodiments, the primepower generator of the system can be any of the closed cycle enginesprovided herein. For instance, any of the embodiments of the balance ofplant described herein can be employed with any of the Stirling enginesprovided herein. In other embodiments, the prime power generator can asolid oxide fuel cell. In further embodiments, the balance of plantembodiments described herein can be employed with any suitable primepower generator.

The balance of plant embodiments of the various power generation systemsdescribed herein can include various features for recovering heatgenerated by the prime power generator and utilizing the recovered heatin some useful way. For example, heat recovered from the prime powergenerator can be used to produce useful work. The useful work can beutilized to drive components of the balance of plant, such ascompressors, pumps, blowers, etc. The recovered heat can also berecirculated to the prime power generator, e.g., to improve theefficiency thereof. Furthermore, in some embodiments, the useful workcan cause one or more electric machines to generate electrical power. Inaddition, recovered heat can be provided to one or more thermalapplications in thermal communication with components of the balance ofplant. The one or more thermal applications can utilize the recoveredheat in any suitable fashion. The provided heat can improve theefficiency of the one or more thermal applications.

In another aspect, various embodiments of Notarniocla cycle systems andcomponents therefore are provided. Generally, the Notarnicola cyclesystems described herein are operable to produce useful work. Theso-called Notarnicola cycle systems operate on a Notarnicola cycle, orstated differently, on a constant density heat addition principle. Forinstance, the Notarnicola cycle systems described herein can include aconstant density heat exchanger operable to hold a volume of workingfluid at constant density during heat application. By applying heat to aworking fluid held at constant density, the temperature and pressure ofthe working fluid can be increased and thus its potential energy can beincreased as well. Advantageously, the increased potential energy of theworking fluid can allow for an expansion device or the like to extractmore useful work therefrom. In some embodiments, the Notarnicola cyclecan include a Wrankel device, or constant density heatexchanger/expansion device, for producing and extracting useful work.The Notarnicola cycle system can be a bottoming-cycle for a closed cycleengine, such as any one of the engines described herein or as astandalone system for producing useful work and/or electrical power.

Notarnicola Cycle System

FIG. 8 provides a schematic view of a Notarnicola cycle system b500operable to produce useful work according to an example embodiment ofthe present disclosure. For this embodiment, the system is a so-calledNotarnicola cycle system b500 that operates on a Notarnicola cycle, orstated differently, on a constant density heat addition principle aswill be explained further below.

The system b500 includes a loop b502. For this embodiment, the loop b502is an open loop. In other embodiments, however, the loop b502 can be aclosed loop. The system b500 includes various elements positioned alongthe loop b502. Particularly, a constant density heat exchanger b510 andan expansion device b504 are positioned along the loop b502. Theexpansion device b504 is positioned downstream of the constant densityheat exchanger b510. The expansion device b504 can be any suitable typeof expansion device b504, such as a turbine rotatable about an axis ofrotation. A working fluid WF is movable through or along the loop b502.Specifically, the working fluid WF is movable through the constantdensity heat exchanger b510 and the expansion device b504 and then canbe exhausted from the system or directed to one or more thermalapplications b140 positioned downstream of the expansion device b504along the loop b502. The working fluid WF can be supercritical fluid,such as e.g., supercritical carbon dioxide. In other embodiments, theworking fluid WF can be any suitable working fluid. A pump can bepositioned along the loop b502 for moving the working fluid WF throughthe loop b502. For instance, the pump can be positioned upstream of theconstant density heat exchanger b510. Alternatively, the working fluidWF can be moved through the loop b502 passively as shown in FIG. 8.

The constant density heat exchanger b510 is positioned in thermalcommunication with a heat source b508. That is, the constant densityheat exchanger b510 is positioned in a heat exchange relationship withthe heat source b508. The heat source b508 can be any suitable type ofheat source b508, such as the cold side b114 and/or hot side b112 of aclosed cycle engine b110 (e.g., one of the Stirling engines describedherein), solar energy, geothermal energy, wind energy, a turbine engine,an internal combustion engine, a battery or battery system, a brakingsystem, some combination thereof, etc. In some embodiments, the heatsource b508 in thermal communication with the constant density heatexchanger b510 can be switched or otherwise changed. For instance, theheat source b508 in thermal communication with the constant density heatexchanger b510 can be switched between a closed cycle engine b110 andsolar energy. As shown, the heat source b508 gives off heat and the heatis captured by a heat sink b512 of the constant density heat exchangerb510, denoted by Q_(IN) in FIG. 8. The captured heat imparts thermalenergy to the working fluid WF flowing through the constant density heatexchanger b510 while the density of the working is held constant orfixed for a predetermined heating time, as will be explained more fullybelow.

The constant density heat exchanger b510 is operatively configured tohold a volume of the working fluid WF at constant density during heatapplication. Stated another way, the constant density heat exchangerb510 is operable to hold a volume of working fluid WF at a fixed densitywhile increasing, via the heat source b508, the temperature and pressureof the working fluid WF. For instance, as depicted in FIG. 8, theconstant density heat exchanger b510 is operable to hold the volume ofworking fluid WF at a fixed density while increasing, via the heatsource b508, i) the temperature of the working fluid WF such that anoutlet temperature T2 of the working fluid WF is greater than the inlettemperature T1 of the working fluid WF; and ii) the pressure of theworking fluid WF such that an outlet pressure P2 of the working fluid WFis greater than the inlet pressure P1 of the working fluid WF. In someembodiments, the constant density heat exchanger b510 can superheat theworking fluid WF. Furthermore, by increasing the pressure of the workingfluid WF in addition to increasing the temperature of the working fluidWF, the potential energy of the working fluid WF can be increased, e.g.,beyond what is achievable by only heating the working fluid WF, andthus, more useful work can be extracted, e.g., by the expansion deviceb504. Further, as will be explained below, a working chamber of theconstant density heat exchanger b510 is configured to iterativelyreceive volumes of working fluid. In some embodiments, at least one ofthe volumes of working fluid received within the working chamber is heldat constant density during heat application. In yet other embodiments,each volume of working fluid received within the working chamber is heldat constant density during heat application.

FIGS. 9 and 10 provide schematic close-up views of one embodiment of aconstant density heat exchanger b510 that can be utilized in the systemof FIG. 8. In some embodiments, the system b500 (FIG. 8) includes one ormore flow control devices. For instance, as depicted, the one or moreflow control devices can include an inlet flow control device b514 andan outlet control device b516. The inlet flow control device b514 ispositioned at an inlet b518 of a working chamber b524 defined by ahousing b522 of the constant density heat exchanger b510. The outletflow control device b516 is positioned at an outlet b520 of the workingchamber b524. The one or more flow control devices b514, b516 arecommunicatively coupled with one or more controllers b526. The one ormore flow control devices b514, b516 can be communicatively coupled withthe one or more controllers b526 in any suitable manner, such as e.g.,by one or more suitable wireless or wired communication links. The oneor more controllers b526 are operatively configured to control the oneor more flow control devices b514, b516. For instance, the one or morecontrollers b526 can send one or more command signals to the flowcontrol devices, e.g., to move them to respective open positions or torespective closed positions. For instance, in FIG. 9, the flow controldevices are shown in an open position in which the working fluid WF canflow into an out of the working chamber b524, and in contrast, in FIG.10, the flow control devices are shown in a closed position in which theworking fluid WF can neither flow into nor out of the working chamberb524.

An example heating cycle at constant or fixed density will now bedescribed. As shown in FIG. 9, the one or more controllers b526 causethe inlet flow control device b514 and the outlet flow control deviceb516 to move to their respective open positions such that a volume ofworking fluid WF can flow out of the working chamber b524 (e.g., from aprevious cycle) and a new volume of working fluid WF can flow into theworking chamber b524. The one or more controllers b526 can cause theinlet flow control device b514 and the outlet flow control device b516to move to their respective open positions substantially simultaneously.In yet other embodiments, the one or more controllers b526 can cause theoutlet flow control device b516 and the inlet flow control device b514to move to their respective open positions in such a way that one flowcontrol device is opened a predetermined lag time behind the other. Forinstance, the one or more controllers b526 can cause the outlet flowcontrol device b516 to move to the open position a predetermined lagtime prior to causing the inlet flow control device b514 to move to theopen position, or vice versa.

After the inlet flow control device b514 and outlet flow control deviceb516 are open for a predetermined open time or upon the working chamberb524 reaching a preselected volume of working fluid WF, the one or morecontrollers b526 cause the inlet flow control device b514 and the outletflow control device b516 to move to their respective closed positions,e.g., as shown in FIG. 10. Notably, with the inlet flow control deviceb514 and the outlet flow control device b516 moved to their respectiveclosed positions, the density of the working fluid WF within the workingchamber b524 is held constant or fixed. That is, the working fluid WF isheld at a constant density. As the working fluid WF is held at constantdensity, the heat source b508 (e.g., the heat source b508 of FIG. 8)applies heat to the working fluid WF within the working chamber b524. Asnoted above, the application of heat to the working fluid WF held atconstant density increases the temperature and pressure of the workingfluid WF, thereby increasing its potential energy.

After heating the working fluid WF at constant density for apredetermined heating time, the one or more controllers b526 cause theinlet flow control device b514 and the outlet flow control device b516to move to their respective open positions. As will be appreciated withreference to FIG. 9, when the flow control devices are moved to theirrespective open positions, the working fluid WF heated at constantdensity exits the working chamber b524 and flows downstream, e.g., tothe expansion device b504 of FIG. 8, and a new volume of working fluidWF flows into the working chamber such that it may be subjected toapplied heat at constant density. The heating cycle continues oriterates during operation of the system.

Returning to FIG. 8, as shown, the expansion device b504 is in fluidcommunication with the constant density heat exchanger b510 and isoperable to receive heated and pressurized working fluid WF therefrom.The expansion device b504 is operable to extract thermal energy from theworking fluid WF to generate useful work, as denoted by W_(OUT). Theextraction of thermal energy from the working fluid WF causes thepressure and temperature of the working fluid WF to decrease. Forinstance, as shown in FIG. 8, the temperature T3 and pressure P3 of theworking fluid WF downstream of the expansion device b504 is less thanthe temperature T2 and pressure P2 upstream of the expansion device b504and downstream of the constant density heat exchanger b510. Theexpansion of the working fluid WF can drivingly rotate the expansiondevice b504 about its axis of rotation. In this way, one or moreelements operatively coupled with the expansion device b504, e.g., via ashaft b506, can be driven as well. In some embodiments, for example, oneor more electric machines b154 can be operatively coupled with theexpansion device b504, and when driven by the expansion device b504, theone or more electric machines b154 can generate electrical power.Additionally or alternatively, in some embodiments, one or more pumps,compressors, blowers, gearboxes, and/or the like can be operativelycoupled with the expansion device b504 and can be driven by theexpansion device b504.

FIG. 11 provides a schematic view of another system operable to produceuseful work according to an example embodiment of the presentdisclosure. For this embodiment, like the system of FIG. 8, the systemis a so-called Notarnicola cycle system b500 that operates on aNotarnicola Cycle or a constant density heat addition principle.

The system includes a loop b502. For this embodiment, the loop b502 is aclosed loop. The system includes various elements positioned along theloop b502. Particularly, a constant density heat exchanger b510, anexpansion device b504, and a pump b528 are positioned along the loopb502. The constant density heat exchanger b510 is positioned between theexpansion device b504 and the pump b528. For this embodiment, theconstant density heat exchanger b510 is positioned downstream of thepump b528 and upstream of the expansion device b504. The expansiondevice b504 can be any suitable type of expansion device b504, such as aturbine rotatable about an axis of rotation. A working fluid WF ismovable through the loop b502. The working fluid WF can be supercriticalfluid, such as e.g., supercritical carbon dioxide. In other embodiments,the working fluid WF can be any suitable working fluid WF.

For this embodiment, the constant density heat exchanger b510 appliesheat to a volume of working fluid WF held at constant density in thesame manner as noted above with respect to the embodiment of FIG. 8. Asthe working fluid WF is held at constant density for a predeterminedheating time during heat application, the flow of working fluid WFexiting the constant density heat exchanger b510 is effectively pulsedout of the constant density heat exchanger b510. For instance, FIG. 12graphically depicts the mass flow rate of the working fluid WF at theoutlet of the constant density heat exchanger b510 as a function oftime. As noted above, the working fluid WF exiting the second heatexchanger exhibits pulse-like characteristics, which is embodied by thestep wave shown in FIG. 12.

In some embodiments, as depicted in FIG. 11, the system includes one ormore pulse converters b532. The one or more pulse converters b532 arepositioned along the loop b502 upstream of the expansion device b504 anddownstream of the constant density heat exchanger b510. Generally, theone or more pulse converters b532 are operable to smooth out or dampenthe pulsed flow of working fluid WF flowing downstream from the constantdensity heat exchanger b510. Particularly, the one or more pulseconverters b532 are operable to dampen the pulsed flow to substantiallya steady-state flow. In this way, the downstream expansion device b504can receive a substantially steady-state flow of working fluid WF. Thiscan create a more steady useful workout by the expansion device b504 andcan reduce undesirable vibration of the expansion device b504, amongother benefits.

Furthermore, in some embodiments, a heat exchanger b530 is positionedalong the loop b502. For this embodiment, the heat exchanger b530 ispositioned downstream of the expansion device b504 and upstream of thepump b528. As shown, the heat exchanger b530 expels heat from theworking fluid WF flowing along the loop b502, denoted by QouT in FIG.11. In this way, the working fluid WF is better able to pick up orextract heat from the heat source b508 downstream thereof.

FIGS. 13 and 14 provide example pulse converters b532 that can beutilized with the system b500 of FIG. 11 and/or the system b500 of FIG.8. As depicted in FIG. 13, in some embodiments, the one or more pulseconverters b532 can be configured as a Venturi-style nozzle having aconverging nozzle b534, a throat b536, and a diverging diffuser b538. Inthe depicted embodiment of FIG. 13, the ejector nozzle b534 convergesthe working fluid WF, thereby increasing the static pressure of theworking fluid WF. The working fluid WF then flows through the throatb536 of the pulse converter b532 and accelerates into the diffuser b538.The working fluid WF slows as it flows along the diffuser b538 anddownstream to the expansion device b504 (FIG. 11). Consequently, thepulsed flow exiting the constant density heat exchanger b510 can besmoothed out. That is, the working fluid WF exhibits a more steady stateflow downstream of the pulse converter b532. Further, as depicted inFIG. 14, in some embodiments, the working fluid WF can enter the pulseconverter b532 through multiple inlet conduits, such as the first inletconduit b535 and a second inlet conduit b537. Although two inletconduits are shown in FIG. 14, it will be appreciated that the workingfluid WF can enter the pulse converter b532 through more than two inletconduits. The multiple inlet conduits can facilitate smoothing of theworking fluid WF by the pulse converter b532.

In some embodiments, at least two of the plurality of pulse convertersb532 can be placed in series. In yet other embodiments, at least two ofthe plurality of pulse converters b532 can be placed in parallel. Insome other embodiments, at least two pulse converters b532 can be placedin parallel with respect to one another and at least two pulseconverters b532 can be placed in series. As noted above, such pulseconverters b532 can dampen the pulsed flow of the working fluid WFexiting the constant density heat exchanger b510.

Returning to FIG. 11, as noted above, the system b500 also includes anexpansion device b504 positioned downstream of the constant density heatexchanger b510. The expansion device b504 is operatively coupled withthe pump b528 in this example embodiment. More specifically, theexpansion device b504 is mechanically coupled with the pump b528 via ashaft b506 or shaft system. Furthermore, the expansion device b504 is influid communication with the constant density heat exchanger b510. Theexpansion device b504 is operable to extract thermal energy from theworking fluid WF to generate useful work, as denoted by W_(OU)T. Theextraction of thermal energy from the working fluid WF causes thepressure and temperature of the working fluid WF to decrease. Theexpansion of the working fluid WF can drivingly rotate the turbine aboutits axis of rotation, which in turn drives the shaft b506 and the pumpb528 operatively coupled thereto. Moreover, when the shaft b506 isdriven by rotation of the turbine, the useful work produced can beutilized to drive other components. In some embodiments, one or moreelectric machines b154 can be operatively coupled with the expansiondevice b504, and when driven by the expansion device b504, the one ormore electric machines b154 can generate electrical power. Additionallyor alternatively, in some embodiments, one or more pumps, compressors,blowers, gearboxes, electric motors, and/or the like can be operativelycoupled with the expansion device b504 and can be driven by theexpansion device b504. After the working fluid WF undergoes expansion atthe expansion device b504, the working fluid WF flows downstream to thepump b528, where the working fluid WF is moved through the loop b502once again.

FIG. 15 provides a schematic view of yet another system operable toproduce useful work according to an example embodiment of the presentdisclosure. The system of FIG. 15 is configured in a similar manner asthe system of FIG. 11 except as provided below. For this embodiment, thesystem includes more than one constant density heat exchangers b510.Particularly, the system includes a plurality of constant density heatexchangers b510 arranged in parallel. The system can include anysuitable number of constant density heat exchangers b510. A single heatsource b508 can give off heat to the constant density heat exchangersb510, or alternatively, a plurality of heat sources b134 can give offheat to the constant density heat exchangers b510. For instance, in someembodiments, each constant density heat exchanger b510 has an associatedheat source b508.

Moreover, for this embodiment, each constant density heat exchanger b510is operable to hold a volume of working fluid WF at constant densityduring heat application, e.g. in a manner described above. Each constantdensity heat exchanger b510 can each include an inlet flow controldevice b514 and an outlet flow control device b516, e.g., as depicted inFIGS. 9 and 10. Notably, one or more controllers b526 of the system cancontrol the timing of the constant density heat exchangers b510 suchthat an inlet b540 of the expansion device b504 receives substantially asteady state flow of working fluid WF. More particularly, the one ormore controllers b526 can cause the opening and closing of the inlet andoutlet flow control devices b514, b516 such that the flow of workingfluid WF flowing downstream to the inlet of the expansion device b504 issubstantially steady state. In this way, the expansion device b504 cangenerate a more constant work output and undesirable vibrationassociated with a pulsed flow can be eliminated or reduced. The timingof the inlet and outlet flow control devices b514, b516 can be set basedat least in part on the number of constant density heat exchangers b510,the distance from the outlet of the working chamber b524 of the constantdensity heat exchangers b510 to the inlet of the turbine, and the massflow of the working fluid WF through the conduits of the loop b502,among other parameters.

Notarnicola Cycle as Bottoming Cycle

FIG. 16 provides a schematic view of a power generation system b550according to an example embodiment of the present disclosure. The powergeneration system b550 includes a prime power generation system b552 anda heat recovery or bottoming-cycle system b554 operable to recover heatfrom the prime power generation system b552 and use the recovered wasteheat to produce useful mechanical work. The mechanical work can be usedfor various applications, such as generating electrical power and/ordriving various elements operatively coupled thereto.

As depicted in FIG. 16, for this embodiment, the prime power generationsystem b552 includes a closed cycle engine operable to produce usefulwork. In other embodiments, the prime power generation system b552 caninclude other suitable types of power generators, including for example,a gas or steam turbine engine, solar panels, etc. The useful workproduced by the closed cycle engine can be used for any suitablepurpose, such as for causing one or more electric machines b154operatively coupled thereto to generate electrical power. The closedcycle engine can be any of the closed cycle engines described herein,including for example, any of the Stirling engines described herein. Aswill be explained further below, heat from the closed cycle engine, orthe waste heat source in this example, can be recovered/extracted andused by the bottoming-cycle system b554 to produce useful mechanicalwork. For instance, heat can be recovered from the cold side and/or thehot side of the closed cycle engine and used by the bottoming-cyclesystem b554 to produce useful mechanical work. The useful work producedby the bottoming-cycle system b554 can be used in turn to drive one ormore elements, such as e.g., a compressor. Moreover, in someembodiments, one or more electric machines can be operatively coupledwith components of the bottoming-cycle system b554. In this way, themechanical work can be used for generating electrical power.Furthermore, notably, the bottoming-cycle system b554 of FIG. 16 is aNotarnicola cycle system that operates on a Notarnicola Cycle, or statedanother way, on a constant density heat addition principle as explainedabove.

FIG. 17 provides a schematic view of a power generation system b550according to an example embodiment of the present disclosure. FIG. 17provides a schematic view of a power generation system b100 according toan example embodiment of the present disclosure. Generally, the powergeneration system b100 of FIG. 17 includes a prime power generationsystem b100 and a balance of plant b200. The balance of plant b200includes a heat recovery system to recover heat from the prime powergeneration system b100. Particularly, the heat recovery system operatesa Rankine-based bottoming cycle to recover heat (e.g., engine exhaust)generated by the prime power generation system b100. The recovered heatcan then be used in a useful way. For instance, the energy recovered bythe heat recovery system can be used to “pay” for pumps and otheraccessories associated with the balance of plant b200 so such componentsdo not rob the closed cycle engine b110 of efficiency. Further, in someembodiments, some or all of the balance of plant b200 components can beadditively manufactured, e.g., by one or more of the additivemanufacturing techniques described herein. In this way, the costsassociated with manufacturing such components can minimized,particularly for relatively smaller mobile applications.

As depicted in FIG. 17, the prime power generation system b100 of thepower generation system b100 is a closed cycle engine b110. The closedcycle engine b110 can be any of the closed cycle engines describedherein. For instance, the closed cycle engine b110 can be one of theStirling engines described herein. The closed cycle engine b110 includesone or more piston assemblies b126 each movable within their respectivepiston bodies b122. Additionally, the closed cycle engine b110 includesa regenerator b120, a hot side heat exchanger b118 operable to heat orimpart thermal energy to the working fluid within the piston bodiesb122, and a cold side heat exchanger b116 operable to remove heat fromthe working fluid within the piston bodies b122. Consequently, theclosed cycle engine b110 generally defines a hot side b112 and a coldside b114. Furthermore, as shown, one or more electric machines b154 areoperatively coupled with the piston assemblies b126. When the pistonassemblies b126 are moved within their respective piston bodies b122,the electric machines b154 are operable to generate electrical power.

Notably for this embodiment, the heater loop b210 of the balance ofplant b200 is positioned at least in part in a heat exchangerelationship with the chiller loop b240 of the balance of plant b200.Accordingly, as will be explained below, heat captured from the hot sideb112 of the engine can be used as a heat source b134 for increasing thetemperature of the chiller working fluid CWF flowing along thebottoming-cycle loop b250 to ultimately increase the potential energythereof. In this way, more or supplemental electrical power can begenerated by the one or more electric machines b262 operatively coupledwith the expansion device b256 of the chiller loop b240. Additionally,heat can be captured from the hot side b112 of the engine and feddirectly back to the engine or to one or more components for increasingthe temperature of fuel and/or air flowing to the combustor b132.

For this embodiment, the heater loop b210 includes a compressor b220positioned along an intake line b212 of the heater loop b210. Thecompressor b220 moves air into the heater loop b210 from an air sourceb218 (e.g., an ambient environment) and pressurizes the air. Arecuperator b222 is positioned downstream of the compressor b220 alongthe intake line b212 of the heater loop b210 as well as along a heatrecovery loop b214 of the heater loop b210. The air pressurized by thecompressor b220 flows downstream to the recuperator b222 along theintake line b212 where the pressurized air is pre-heated by hotcombustion gases recovered from the closed cycle engine b110, or moreparticularly, from the hot side heat exchanger b118 of the closed cycleengine b110. As the pressurized and now pre-heated air flows downstream,the pressurized/pre-heated air combines or mixes with hot combustiongases recirculated from the hot side heat exchanger b118, e.g., via arecirculation loop b216 of the heat recovery loop b214.

The heated air mixes with fuel and the fuel/air mixture is combusted ina combustor b132 or burner of the closed cycle engine b110. Thecombustion gases generated by the combustion process are provided to thehot side heat exchanger b118 via the intake line b212. The hot side heatexchanger b118 facilitates heat exchange between the hot combustiongases and the engine working fluid EWF within the piston body b122. Theheat imparted to the engine working fluid EWF creates a temperaturedifferential between the hot side b112 and the cold side b114 of theclosed cycle engine b110. The expansion and compression of the engineworking fluid EWF causes the piston assemblies b126 to move within theirrespective piston bodies b122, thereby producing useful work. The usefulmechanical work can be converted into electrical power, e.g., by the oneor more electric machines b154 operatively coupled with the pistonassemblies b126.

After the relatively hot combustion gases impart thermal energy to theengine working fluid EWF within the piston body b122, the combustiongases are captured and directed downstream along the heat recovery loopb214 for further useful purposes. For instance, a portion of thecombustion gases are recirculated via the recirculation loop b216 backto the combustor b132 and a portion of the combustion gases are used toimpart thermal energy to the pressurized air passing through therecuperator b222. That is, a portion of the combustion gases are used topreheat the incoming pressurized air at the recuperator b222.

After flowing through the recuperator b222, the hot combustion gasesrecovered from the hot side heat exchanger b118 of the closed cycleengine b110 continue downstream along the heat recovery loop b214 to theconstant density heat exchanger b560 of the chiller loop b240. Thus, asnoted above, the heater loop b210 is at least in part in a heat exchangerelationship with the chiller loop b240. Particularly, for thisembodiment, the heater loop b210 is at least in part in a heat exchangerelationship with the chiller loop b240 at the constant density heatexchanger b560. The hot combustion gases heat or impart thermal energyto the chiller working fluid CWF flowing through the bottoming-cycleloop b250 at the constant density heat exchanger b560. In this way, thetemperature of the chiller working fluid CWF is increased even furtherprior to expanding at the expansion device b256 downstream of theconstant density heat exchanger b560. The increased potential energy ofthe chiller working fluid CWF allows the expansion device b256 toextract more useful work therefrom. Accordingly, more electrical powercan be generated by the one or more electric machines b262 operativelycoupled with the expansion device b256.

After imparting thermal energy to the chiller working fluid CWF at theconstant density heat exchanger b560, the combustion gases flowdownstream along the heat recovery loop b214 to the fuel preheater b304.The combustion gases impart thermal energy to fuel flowing downstreamalong a fuel line 302 from a fuel source b300 (e.g., a fuel tank) at thefuel preheater b304. In this way, the fuel can be preheated prior tobeing mixed with the heated/pressurized air. Preheating the fuel priorto mixing with the heated/pressurized air can reduce the amount of fuelrequired for the same work output. After heat exchange at the fuelpreheater b304, the combustion gases flow downstream along the heatrecovery loop b214 of the heater loop b210 and are exhausted from thesystem.

Notably, for this embodiment, the heat recovered from the hot side heatexchanger b118 is exchanged with the various elements along the heaterloop b210 in an ordered manner to achieve high efficiency of the powergeneration system b100. For instance, for the depicted embodiment ofFIG. 17, the thermal energy generated by the combustor b132 is firstused by the hot side heat exchanger b118 to heat the engine workingfluid EWF within the piston body b122. Thereafter, the hot combustiongases continue downstream. Some of the recovered combustion gases aredirected back to the combustor b132 via the recirculation loop b216 andsome of the combustion gases are directed to the recuperator b222 forpre-heating the compressed air, which also returns heat to the engine.Next, the hot combustion gases are used to heat the chiller workingfluid CWF flowing along the bottoming-cycle loop b250 at the constantdensity heat exchanger b560. The hot combustion gases are then used topre-heat the fuel at the fuel preheater b304, thereby returning heat tothe engine. Finally, the combustion gases are exhausted from the system.

The chiller loop b240 of the balance of plant b200 is operable to removeheat or thermal energy from the cold side b114 of the closed cycleengine b110. Particularly, a working fluid can be passed through thecold side heat exchanger b116. The engine working fluid EWF can exchangeheat with the relatively cool working fluid flowing through the coldside heat exchanger b116, and thus, the working fluid removes heat fromthe closed cycle engine b110 to provide cooling thereto, e.g., at thecold side b114. The cooled engine working fluid EWF facilitatescompression thereof when the piston assembly b126 is moved toward thecompression space by the expansion of the working fluid at the other endof the regenerative engine.

As illustrated in FIG. 17, the chiller loop b240 includes two linkedloops, including a bottoming-cycle loop b250 and a cooling loop b280.The bottoming-cycle loop b250 or system is a recovered heat to powersystem. Particularly, a chiller working fluid CWF, such as e.g., asupercritical carbon dioxide or some other suitable low temperatureworking fluid, is moved through the bottoming-cycle loop b250 to removeheat from the cold side b114 of the engine (e.g., to increase thetemperature differential between the hot and cold sides of the engine).Components of the bottoming-cycle loop b250 utilize the captured heat togenerate electrical power. The cooling loop b280 is operable to coolcertain components positioned along the bottoming-cycle loop b250.Specifically, a cooling fluid CF, such as e.g., ambient air or someother suitable heat-sink fluid, is moved through the cooling loop b280and exchanges heat with the various components of the bottoming-cycleloop b250 to provide cooling thereto. The chiller loop b240 will bedescribed in detail below.

For this embodiment, the bottoming-cycle loop b250 of the chiller loopb240 includes a pump b252 operable to move the chiller working fluid CWFalong or through the bottoming-cycle loop b250. As noted above, thechiller working fluid CWF can be a supercritical carbon dioxide fluid orsome other suitable low temperature working fluid. A precooler b260 isoptionally positioned downstream of the pump b252 along thebottoming-cycle loop b250. The precooler b260 cools the chiller workingfluid CWF as the chiller working fluid CWF flows therethrough. The coldside heat exchanger b116 (e.g., an evaporator) is positioned downstreamof the precooler b260 along the bottoming-cycle loop b250. The cold sideheat exchanger b116 is positioned in a heat exchange relationship withthe cold side b114 of the closed cycle engine b110 as shown in FIG. 17.During operation of the closed cycle engine b110, the chiller workingfluid CWF flowing through the cold side heat exchanger b116 picks up orremoves heat from the engine working fluid EWF and walls of the pistonbody b122 at or proximate the cold side b114 of the engine b110. Thatis, the engine working fluid EWF and walls at or proximate the cold sideb114 of the engine b110 impart thermal energy to the chiller workingfluid CWF flowing through the cold side heat exchanger b116.Accordingly, the heat captured from the cold side b114 of the engineb110 can be utilized to generate electrical power and/or produce usefulwork.

In some embodiments, optionally, the relatively hot chiller workingfluid CWF flows downstream from the cold side heat exchanger b116 to aconstant density heat exchanger b560 or second heat exchanger positionedalong the bottoming-cycle loop b250. For this embodiment, the heatsource b134 that imparts thermal energy to the chiller working fluid CWFflowing through the bottoming-cycle loop b250 at the constant densityheat exchanger b560 is the hot combustion gases flowing along the heatrecovery loop b214 of the heater loop b210. Accordingly, heat recoveredfrom the hot side b112 of the engine is utilized for electrical powergeneration.

An expansion device b256 is positioned downstream of the cold side heatexchanger b116 along the bottoming-cycle loop b250. In some embodiments,the expansion device b256 is immediately downstream of the cold sideheat exchanger b116. In yet other embodiments, as noted above, theexpansion device b256 is downstream of the cold side heat exchanger b116but directly downstream of the constant density heat exchanger b560. Theexpansion device b256 can be a turbine, for example. The expansiondevice b256 can be operatively coupled with one or more elements of thechiller loop b240 and/or the heater loop b210. For instance, theexpansion device b256 can be mechanically coupled with the pump b252 ofthe bottoming-cycle loop b250, the compressor b220 of the heater loopb210, and/or a fan b284 of the cooling loop b280 of the chiller loopb240, among other components. The expansion device b256 can bemechanically coupled with such components via one or more shafts or ashaft system. The expansion device b256 is operable to extract thermalenergy from the chiller working fluid CWF to produce useful work suchthat electrical power can be generated. Particularly, the expansion ofthe chiller working fluid CWF can drivingly rotate the expansion deviceb256 about its axis of rotation, which in turn drives the one or moreshafts and the components operatively coupled thereto. Moreover, whenthe shaft system is driven by rotation of the expansion device b256, theuseful work produced can be utilized to drive one or more electricmachines b262 operatively coupled to the expansion device b256. In thisway, the electric machines b262 can generate electrical power. Theelectrical power generated can be used to pay or operate the variousdevices or components of the power generation system b100, such as e.g.,fans, pumps, outside air conditioning units, onboard vehicle systems,among other potential uses.

After expanding at the expansion device b256 to produce useful work suchthat electrical power can ultimately be generated, the chiller workingfluid CWF flows downstream from the expansion device b256 to a thirdheat exchanger b258 or third heat exchanger positioned along thebottoming-cycle loop b250. The third heat exchanger b258 is positionedbetween the expansion device b256 and the pump b252 along thebottoming-cycle loop b250. The third heat exchanger b258 cools thechiller working fluid CWF before the chiller working fluid CWF flowsdownstream to the pump b252 where the chiller working fluid CWF ispumped or moved along the bottoming-cycle loop b250 once again.

As noted above, the chiller loop b240 includes the cooling loop b280linked to the bottoming-cycle loop b250. As depicted in FIG. 17, thecooling fluid CF is introduced into the cooling loop b280 at theprecooler b260 via a pressure differential. The relatively cool coolingfluid CF can pick up or remove heat from the chiller working fluid CWFflowing through the bottoming-cycle loop b250 at the precooler b260.That is, the chiller working fluid CWF of the bottoming-cycle loop b250can impart thermal energy to the cooling fluid CF of the cooling loopb280 at the precooler b260. In addition, cooling fluid CF is introducedinto the cooling loop b280 at the third heat exchanger b258 via apressure differential. The relatively cool cooling fluid CF can pick upheat from the chiller working fluid CWF flowing through thebottoming-cycle loop b250 at the third heat exchanger b258. That is, thechiller working fluid CWF flowing along the bottoming-cycle loop b250can impart thermal energy to the cooling fluid CF of the cooling loopb280 at the third heat exchanger b258. As illustrated in FIG. 17, thecooling fluid CF can flow downstream from the precooler b260 anddownstream from the third heat exchanger b258 to a fan b284 positionedalong the cooling loop b280. The fan b284 moves the cooling fluid CFthrough the cooling loop b280. Particularly, the fan b284 can cause thepressure differential at the inlet of the precooler b260 and the inletof the third heat exchanger b258 such that the cooling fluid CF is movedinto and through the cooling loop b280 of the chiller loop b240. Afterremoving heat from the chiller working fluid CWF flowing through thebottoming-cycle loop b250 at the precooler b260 and the third heatexchanger b258, the cooling fluid CF is exhausted from the system.

The chiller working fluid CWF flowing through the bottoming-cycle loopb250 at the superheater b560 can be held at constant density during heatapplication to increase the temperature and pressure of the chillerworking fluid CWF. The hot combustion gases or heating working fluid HWFflowing through the heat recovery loop b214 apply heat to the chillerworking fluid CWF held at constant density at the superheater b560.

Returning to FIG. 18, as noted above, the bottoming-cycle system b554embodied as a Notarnicola cycle system b500 also includes an expansiondevice b256 positioned downstream of the constant density superheaterb560. The expansion device b256 can be a turbine, for example. Theexpansion device b256 is operatively coupled with the pump b252 in thisexample embodiment. More specifically, the expansion device b256 ismechanically coupled with the pump b252 via a shaft or shaft system.Furthermore, the expansion device b256 is in fluid communication withthe constant density superheater b560. The expansion device b256 isoperable to extract thermal energy from the chiller working fluid CWF togenerate useful work, as denoted by W_(OUT). Particularly, the expansionof the chiller working fluid CWF can drivingly rotate the expansiondevice b256 about its axis of rotation, which in turn drives the shaftand the pump b252 operatively coupled thereto. Moreover, when the shaftis driven by rotation of the expansion device b256, the useful workproduced can be utilized to drive other components. For example, theuseful work produced can drive a compressor of the closed cycle engineb110 operatively coupled with the expansion device b256 via a shaft.Consequently, waste heat from the closed cycle engine b110 can beutilized to produce work that can ultimately be utilized for driving oneor more components of the closed cycle engine b110, such as e.g.,compressors, fans, pumps, etc. Furthermore, for this embodiment, one ormore electric machines b262 are operatively coupled with the expansiondevice b256. Accordingly, when the expansion device b256 is driven aboutits axis of rotation by expansion of the chiller working fluid CWF, theelectric machines b262 operatively coupled with the expansion deviceb256 can generate electrical power.

When the working fluid exits the expansion device b256, the workingfluid has a pressure P4 and a temperature T4. As depicted in FIG. 18,the pressure P4 is greater than the pressure P1 but less than thepressure P3. The pressure P4 is less than the pressure P3 due to theextraction of the energy from the working fluid by the expansion deviceb256. The temperature T4 is greater than the temperature T1 but lessthan the temperature T3. The temperature T4 is less than the temperatureT3 due to the extraction of energy from the working fluid by theexpansion device b256.

The system b554 also includes a third heat exchanger or third heatexchanger b258 positioned along the bottoming-cycle loop b250. The thirdheat exchanger b258 has an inlet and an outlet. The inlet of the thirdheat exchanger b258 is in fluid communication with the expansion deviceb256 and the outlet of the third heat exchanger b258 is in fluidcommunication with the pump b252. Accordingly, the third heat exchangerb258 is positioned downstream of and is in fluid communication with theexpansion device b256 and the third heat exchanger b258 is positionedupstream of and is in fluid communication with the pump b252. Thus, thethird heat exchanger b258 receives the working fluid from the expansiondevice b256 and the pump b252 receives the working fluid from the thirdheat exchanger b258. The third heat exchanger b258 is operable todecrease the temperature of the working fluid. In this way, the workingfluid is better able to extract heat from the cold side b114 of theengine. As depicted, the third heat exchanger b258 is operable todecrease the temperature of the working fluid to a temperature T1, whichis less than the temperature T4, the temperature T3, and the temperatureT2. As the temperature decreases, the pressure of the working fluiddecreases as well. As depicted, the pressure of the working fluiddecreases to P1 which is less than the pressure P4, the pressure P3, andthe pressure P2. A cooling fluid CF (e.g., air) flowing along thecooling loop b280 can be passed through the third heat exchanger b258 toremove heat from the chiller working fluid CWF flowing therethrough.

FIG. 19 depicts the advantages of the constant density heat applicationprocess described above. Particularly, FIG. 19 depicts a T-s diagram(i.e., a temperature-entropy diagram) of the closed cycle engine b110utilizing the advantages of the constant density heat applicationprocess described above. As shown, using the constant density heatexchange process during super heating or reheating of the working fluidleads to a higher turbine inlet temperature, and therefore, more workout. This can be seen particularly on the T-s diagram where the constantdensity super heating causes the working fluid to increase isobars intemperature compared to a baseline system without constant density heatapplication. One benefit of the constant density heat exchange processis an increase of nearly twice the temperature difference across theexpansion device b256 (FIG. 18) or turbine.

FIG. 20 provides a schematic view of another power generation systemb580 according to an example embodiment of the present disclosure. Thepower generation system b580 depicted in FIG. 20 has a similarconfiguration to the system b550 of FIG. 18 except as provided below.Notably, for this embodiment, the cold side heat exchanger is a constantdensity heat exchanger b582. The cold side constant density heatexchanger b582 can be configured and can operate in the same or similarmanner as described above. As depicted, the heat source can be the heatextracted from the cold side b114 of the closed cycle engine b110.

FIG. 21 provides a schematic view of another power generation systemb590 according to an example embodiment of the present disclosure. Thepower generation system b590 depicted in FIG. 21 has a similarconfiguration to the system b550 of FIG. 18, except as provided below.Notably, for this embodiment, the cold side heat exchanger and thesuperheater are both constant density heat exchangers. Thus, the coldside heat exchanger is a constant density cold side heat exchanger b582and the superheater is a constant density superheater b560. The coldside constant density heat exchanger b582 and the constant densitysuperheater b560 can be configured and can operate in the same orsimilar manner as the constant density heat exchangers described above.

As shown in FIG. 21, for instance, the constant density cold side heatexchanger b582 is operable to hold a volume of working fluid (e.g.,chiller working fluid CWF) at fixed density while increasing, via theheat source b508, the temperature and pressure of the working fluid.Particularly, the constant density cold side heat exchanger b582 isoperable to hold the volume of working fluid at a fixed density whileincreasing, via the heat source (e.g., the heat extracted from the coldside b114 of the engine), i) the temperature of the working fluid suchthat an outlet temperature T2 of the working fluid is greater than theinlet temperature T1 of the working fluid; and ii) the pressure of theworking fluid such that an outlet pressure P2++ of the working fluid isgreater than the inlet pressure P2 of the working fluid. Thus, insteadof a pressure drop across the cold side heat exchanger b116 (e.g., asoccurs in the depicted embodiment of FIG. 18), the pressure of theworking fluid is increased, e.g., from P2 to P2++).

Furthermore, the constant density superheater b560 is operable to hold avolume of working fluid at fixed density while increasing, via the heatsource b508, the temperature and pressure of the working fluid flowingalong the bottoming-cycle loop b250. Particularly, the constant densitysuperheater b560 is operable to hold the volume of working fluid at afixed density while increasing, via the heat source b508 (e.g., wasteheat from the hot side b112 of the closed cycle engine b110 and/or someother source), i) the temperature of the working fluid such that anoutlet temperature T3 of the working fluid is greater than the inlettemperature T2 of the working fluid; and ii) the pressure of the workingfluid such that an outlet pressure P3 of the working fluid is greaterthan the inlet pressure P2++ of the working fluid. By increasing thepressure of the working fluid at the constant density cold side heatexchanger b582 and at the constant density superheater b560, thepotential energy of the working fluid can be increased beyond what isachievable simply by heating the working fluid or by increasing itspressure by a single constant density heat exchanger, and thus, moreuseful work can be extracted, e.g., by the expansion device b256.

FIG. 22 provides a schematic view of a power generation system b100according to an example embodiment of the present disclosure. FIG. 22 isconfigured in a similar manner as the power generation system b100 ofFIG. 17, except as provided below.

For this embodiment, a Notarnicola cycle system b500 is positioned alongthe heater loop b210. Particularly, the Notarnicola cycle system b500 ispositioned along the heat recovery loop b214 of the heater loop b210. Asdepicted, a constant density heat exchanger b602 is positioneddownstream of the fuel preheater b304 along the heat recovery loop b214.A turbine b604 or expansion device is positioned downstream of theconstant density heat exchanger b602 along the heat recovery loop b214.In some embodiments, a pulse converter b532 can be positioned betweenthe constant density heat exchanger b602 and the turbine b604, e.g., forsmoothing out or dampening the pulses of working fluid. Combustion gasesor heating working fluid HWF flowing along the heat recovery loop b214can flow through the constant density heat exchanger b602. In someembodiments, the constant density heat exchanger b602 can hold a volumeof combustion gases at constant density during heat application, e.g.,by a heat source as denoted by Q_(IN) in FIG. 22. The working chamber ofthe constant density heat exchanger b602 can iteratively receive volumesof combustion gases and hold or trap them at constant density duringheat application. After a volume of combustion gases is heated atconstant density, the volume of combustion gases can then flowdownstream to the turbine b604 such that the turbine b604 can extractthermal energy therefrom to produce useful work. One or more electricmachines b154 operatively coupled with the turbine b604 can thengenerate electrical power. After expansion of the combustion gases atthe turbine b604, the combustion gases can be exhausted from the system,e.g., to an ambient environment, and/or can flow downstream to one ormore thermal applications b140.

In other embodiments, the combustion gases can be used as the heatsource b508 for applying heat to a working fluid flowing through theconstant density heat exchanger b602. For instance, a working fluid(e.g., ambient air) can be passed through the constant density heatexchanger b602 and held at constant density while the heat from theheating working fluid HWF (e.g., combustion gases) heats or impartsthermal energy to the working fluid. In this way, the temperature andpressure of the working fluid can be increased and thus its potentialenergy can be increased as well. The working fluid can then flowdownstream to an expansion device. The expansion device can extractthermal energy from the working fluid to produce useful work. One ormore electric machines b154 operatively coupled with the turbine b604can then generate electrical power. After expansion of the working fluidat the turbine b604, the working fluid can be exhausted from the system,e.g., to an ambient environment, and/or can flow downstream to one ormore thermal applications b140. Similarly, the combustion gases can beexhausted from the system, e.g., to an ambient environment, and/or canflow downstream to one or more thermal applications b140.

FIG. 23 provides a schematic view of another system operable to produceuseful work according to an example embodiment of the presentdisclosure. For this embodiment, the system is a Notarnicola cyclesystem b500 that operates on a Notarnicola cycle, or stated another way,on a constant density heat addition principle.

The system includes a loop b502. For this embodiment, the loop b502 isan open loop. In other embodiments, however, the loop b502 can be aclosed loop. A working fluid WF is movable through the loop b502. Theworking fluid WF can be supercritical fluid, such as e.g., supercriticalcarbon dioxide. In other embodiments, the working fluid WF can be anysuitable working fluid WF, such as air. Notably, for this embodiment,the functions of the constant density heat exchanger and the expansiondevice are combined into a single device positioned along the loop b502,referred to herein as a constant density heat exchanger expansiondevice, or more concisely stated, a “Wrankel device b800.”

The Wrankel device b800 is positioned in thermal communication with aheat source b508. That is, the Wrankel device b800 is positioned in aheat exchange relationship with the heat source b508. The heat sourceb508 can be any suitable type of heat source b508, such as the cold sideb114 and/or hot side b112 of a closed cycle engine b110 (e.g., one ofthe Stirling engines described herein), solar energy, geothermal energy,wind energy, a turbine engine, an internal combustion engine, a batteryor battery system, a braking system, some combination thereof, etc. Insome embodiments, the heat source b508 in thermal communication with theWrankel device b800 can be switched or otherwise changed. For instance,the heat source b508 in thermal communication with the Wrankel deviceb800 can be switched between a closed cycle engine b110 and solarenergy. As shown, the heat source b508 gives off heat and the heat iscaptured by the Wrankel device b800, denoted by Q_(IN) in FIG. 23. Thecaptured heat imparts thermal energy to the working fluid WF flowingthrough the Wrankel device b800 while the density of the working is heldconstant or fixed for a predetermined heating time. That is, the Wrankeldevice b800 is operable to hold a volume of working fluid WF movingthrough the loop b502 at constant density during heat application. Inthis way, the pressure and temperature of the working fluid WF isincreased, which ultimately increases the potential energy of theworking fluid WF.

The Wrankel device b800 then facilitates expansion of the volume ofworking fluid WF held at constant density during heat application. Inthis manner, the Wrankel device b800 can produce useful work. Forinstance, the expansion of the working fluid WF can drive a shaft b802of the Wrankel device b800 about its axis of rotation. In someembodiments, one or more components can be operatively coupled to theshaft b802 such that they are driven by the Wrankel device b800. Afterthe Wrankel device b800 extracts energy from the working fluid WF duringexpansion to produce useful work, the working fluid WF is exhausteddownstream of the Wrankel device b800. In some embodiments, the workingfluid WF can be used to provide a heat source b508 to one or morethermal applications b140 downstream of the Wrankel device b800.

FIG. 24 provides a schematic view of another system operable to produceuseful work according to an example embodiment of the presentdisclosure. For this embodiment, the system is a Notarnicola cyclesystem b500 that operates on a Notarnicola cycle or a constant densityheat addition principle. FIG. 24 is configured in a similar manner asthe power generation system b100 of FIG. 18, except as provided below.

For this embodiment, the Notarnicola cycle system b500 is abottoming-cycle system b250 of a closed cycle engine b110, such as anyof the closed cycle engines described herein. Further, notably, thesuperheater and the expansion device are combined into a Wrankel deviceb800 in this embodiment. That is, the superheater and the expansiondevice are combined into a single device that functions as a constantdensity heat exchanger and expansion device.

The Wrankel device b800 is positioned in thermal communication with aheat source, which is the heating working fluid HWF (e.g., hotcombustion gases) flowing along the heat recovery loop b214 of theheater loop b210. That is, the Wrankel device b800 is positioned in aheat exchange relationship with the hot combustion gases flowing alongthe heat recovery loop b214. As shown, the hot combustion gases give offheat and the heat is captured by the Wrankel device b800, denoted byQ_(IN) 2 in FIG. 24. The captured heat imparts thermal energy to thechiller working fluid CWF flowing through the Wrankel device b800 whilethe density of the working is held constant or fixed for a predeterminedheating time. That is, the Wrankel device b800 is operable to hold avolume of chiller working fluid CWF moving through the loop b250 atconstant density during heat application. In this way, the pressure andtemperature of the chiller working fluid CWF is increased, whichultimately increases the potential energy of the chiller working fluidCWF. In some embodiments, the Wrankel device b800 is operable tosuperheat the chiller working fluid CWF held at constant density.

The Wrankel device b800 then facilitates expansion of the volume ofchiller working fluid CWF held at constant density during heatapplication. In this manner, the Wrankel device b800 can produce usefulwork. For instance, the expansion of the chiller working fluid CWF candrive a shaft of the Wrankel device b800 about its axis of rotation. Insome embodiments, one or more components can be operatively coupled tothe shaft such that they are driven by the Wrankel device b800. Forinstance, for this embodiment, one or more electric machines b262 areoperatively coupled with the Wrankel device b800 via the shaft or shaftsystem. Accordingly, when the shaft is driven about its axis ofrotation, the one or more electric machines b262 operatively coupledthereto are configured to generate electrical power. After the Wrankeldevice b800 extracts energy from the chiller working fluid CWF duringexpansion to produce useful work and ultimately electrical power, thechiller working fluid CWF is moved downstream to the third heatexchanger b258 where the chiller working fluid CWF is cooled, e.g., bycooling fluid CF flowing through the cooling loop b280. Next, the cooledchiller working fluid CWF flows downstream to the pump b252. The pumpb252 moves the chiller working fluid CWF through the bottoming-cycleloop b250. After flowing through the pump b252, the chiller workingfluid CWF picks up or extracts heat from the cold side b114 of theclosed cycle engine b110, e.g., to provide cooling thereto. Thereafter,as noted above, the chiller working fluid CWF flows downstream to theWrankel device b800.

Linear Constant Density Heat Exchanger

FIG. 25 provides a schematic cross-sectional view of a linear constantdensity heat exchanger b650 according to an aspect of the presentdisclosure. Generally, the linear constant density heat exchanger b650is operable to hold a volume of working fluid at constant density for apredetermined heating time while heat is applied to the working fluid.The linear constant density heat exchanger b650 can be implemented inany of the embodiments of the Notarnicola cycle system b500 and/or anyof the systems described herein. For reference, the linear constantdensity heat exchanger b650 defines an axial direction A, a radialdirection R, a circumferential direction C, and an axial centerline ACextending along the axial direction A. The radial direction R extends toand from the axial centerline AC in a direction orthogonal to the actualdirection A. The circumferential direction C extends 360° around theaxial centerline AC.

The linear constant density heat exchanger b650 includes a housing b652defining at least a portion of a working chamber b654 operable toreceive a working fluid therein. The working fluid is denoted in FIG. 25as “WF” and can be any suitable fluid. For instance, in someembodiments, the working fluid WF is a supercritical fluid. For example,in some embodiments, the working fluid WF is a supercritical carbondioxide. For the depicted embodiment of FIG. 25, the housing b652 istubular. The tubular housing b652 is elongated and extends between afirst end b660 and a second end b662 along the axial direction A. Thefirst end b660 of the tubular housing b652 is connected to (e.g.,threadingly engaged with) an inlet port b664. The inlet port b664 is inturn connected to (e.g., threadingly engaged with) an inlet housingb667. The inlet port b664 is also connected to (e.g., threadinglyengaged with) an inlet conduit b670 that provides a means for theworking fluid to flow into the linear constant density heat exchangerb650. In addition, the inlet housing b667 is connected to (e.g.,threadingly engaged with) a first heat exchanger port b672, which inthis embodiment is an outlet heat exchanger port in this embodiment. Aswill be explained further below, a heat exchange fluid HXF flowingthrough the linear constant density heat exchanger b650 can exit theconstant density heat exchanger via the first heat exchanger port b672.The heat exchange fluid HXF can be any suitable type of fluid. Forinstance, as one example, the heat exchange fluid HXF can be combustiongases flowing along a heat recovery loop b214. The inlet housing b667defines an inlet chamber b668 operable to receive the tubular housingb652, as well as a portion of the inlet port b664 and a portion of thefirst heat exchanger port b672. Furthermore, a heater housing b688 isalso connected to (e.g., threadingly engaged with) the inlet housingb667.

The linear constant density heat exchanger b650 also includes an outlethousing b678 spaced from the inlet housing b667 along the axialdirection A. The outlet housing b678 defines an outlet chamber b680operable to receive at least portion of the tubular housing b652therein. The second end b662 of the tubular housing b652 is connected to(e.g., threadingly engaged with) an outlet port b676. The outlet portb676 is in turn connected to an outlet housing b678. The outlet portb676 is also connected to (e.g., threadingly engaged with) an outletconduit b682 that provides a means for the working fluid to flow out ofor exit the linear constant density heat exchanger b650. In addition,the outlet housing b678 is connected to (e.g., threadingly engaged with)a second heat exchanger port b684, which in this embodiment is an inletheat exchanger port, labeled as the second heat exchanger port b684 inFIG. 25. As will be explained further below, a heat exchange fluid HXFflowing through the linear constant density heat exchanger b650 canenter the heat exchanger via the second heat exchanger port b684. Theoutlet housing b678 defines an outlet chamber b680 operable to receiveat least a portion of the tubular housing b652, as well as a portion ofthe outlet port b676 and a portion of the second heat exchanger portb684. The heater housing b688 is also connected to (e.g., threadinglyengaged with) the outlet housing b678.

The heater housing b688 extends between the inlet housing b667 and theoutlet housing b678 along the axial direction A, and as noted above, theheater housing b688 is connected to (e.g., threadingly engaged with) theinlet housing b667 at one end and the outlet housing b678 at itsopposite end. Notably, the heater housing b688 annularly surrounds thetubular housing b652 between the inlet housing b667 and the outlethousing b678. That is, the heater housing b688 extends annularly aroundthe tubular housing b652 at least between the inlet housing b667 and theoutlet housing b678 along the axial direction A. An annular orring-shaped heat exchange chamber b690 is defined between the heaterhousing b688 and the tubular housing b652. However, in some embodiments,the heat exchange chamber b690 need not be annular. The heat exchangechamber b690 provides fluid communication between the inlet chamber b668defined by the inlet housing b667 and the outlet chamber b680 defined bythe outlet housing b678. In this way, heat exchange fluid HXF can flowtherebetween and impart heat or thermal energy to the working fluidcontained within the working chamber b654. Stated another way, heatexchange fluid HXF can enter the linear constant density heat exchangerb650 through second heat exchanger port b684 and can flow downstreaminto the outlet chamber b680 defined by the outlet housing b678. Theheat exchange fluid HXF can then flow further downstream into the heatexchange chamber b690 defined between the radially outer surface of thetubular housing b652 and the inner radial surface of the heater housingb688. The heat exchange fluid HXF can flow along the axial direction Athrough the heat exchange chamber b690 of the tubular housing b652. Inthis example embodiment, the heat exchange fluid HXF flows from right toleft in FIG. 25. The heat exchange fluid HXF eventually flows downstreaminto the inlet chamber b668 defined by the inlet housing b667. The heatexchange fluid HXF then exits the linear constant density heat exchangerb650 via the first heat exchanger port b672. In alternative embodiments,the linear constant density heat exchanger b650 can be configured suchthat the heat exchange fluid HXF flows from left to right in thedepicted embodiment of FIG. 25.

The linear constant density heat exchanger b650 also includes one ormore flow control devices operable to selectively allow a volume ofworking fluid to enter and exit the working chamber b654. In thisexample embodiment, the flow control devices are valves. The one or morevalves include a first valve b674 or first flow control device and asecond valve b686 or second flow control device. The first valve b674 ispositioned along the inlet conduit b670 at or proximate the inlet of theconstant density heat exchanger and the second valve b686 is positionedalong the outlet conduit b682 at the outlet of the constant density heatexchanger. In some embodiments, the first valve b674 and the secondvalve b686 are both solenoid valves. However, in other embodiments, thefirst and second valve b674, b686 can be other suitable types of valves.

Moreover, as depicted, the working chamber b654 has an inlet and anoutlet. In some embodiments, the inlet and the outlet of the workingchamber b654 are defined by the tubular housing b652, e.g., at the firstend b660 and the second end b662, respectively. In yet otherembodiments, the inlet and the outlet of the working chamber b654 aredefined by other components of the linear constant density heatexchanger b650. For instance, for the depicted embodiment of FIG. 25,the inlet of the working chamber b654 is defined by the inlet conduitb670 immediately downstream of the first valve b674 and the outlet ofthe working chamber b654 is defined by the outlet conduit b682immediately upstream of the second valve b686. The first valve b674 ismovable between an open position and a closed position. Likewise, thesecond valve b686 is movable between an open position and a closedposition. In some embodiments, the one or more valves arecommunicatively coupled with one or more controllers b692. The one ormore controllers b692 can cause the valves to move between theirrespective open and closed positions. The one or more controllers b692can cause the valves to open and/or close simultaneously or at offsettimes from one another.

An example manner in which the linear constant density heat exchangerb650 can heat working fluid held at constant density will now bedescribed. That is, an example heating cycle will now be described. Insome embodiments, the one or more controllers b692 are configured tocause the first valve b674 and the second valve b686 to move to theirrespective open positions such that a first volume of working fluidflows into the working chamber b654. As this occurs, a volume of workingfluid heated while held at constant density during a previous heatingcycle exits the working chamber b654. That is, in causing the firstvalve b674 and the second valve b686 to move to their respective openpositions, a new or unheated volume of working fluid flows into theworking chamber b654 while the volume of working fluid heated atconstant density during a previous heating cycle flows out of theworking chamber b654. Thus, when the valves are moved to theirrespective open positions, a volume of working fluid heated at constantdensity exits the working chamber b654 and a non-heated volume ofworking fluid enters the working chamber b654.

After a predetermined open time has elapsed, the one or more controllersb692 cause the first valve b674 and the second valve b686 to move totheir respective closed positions such that a volume of working fluid iscontained within the working chamber b654 at constant density. The firstand second valves b674, b686 can be closed simultaneously. With thedensity of the working fluid held constant within the working chamberb654, the heat exchange fluid HXF flowing through the heat exchangechamber b690 heats or imparts thermal energy to the working fluid heldat constant density for a predetermined heating time (e.g., about fiveseconds, about one second, about 250 milliseconds, etc.). For instance,the heat exchange fluid HXF can flow serially through the outlet chamberb680, the heat exchange chamber b690, and the inlet chamber b668 asdescribed above (e.g., in a direction generally to the left in FIG. 25).As this occurs, the heat exchange fluid HXF heats the working fluid heldat constant density within the working chamber b654. As the workingfluid is held at constant density within the working chamber b654 duringheat application, the temperature and pressure of the working fluidincreases. The increased temperature and pressure of the working fluidincreases the potential energy of the working fluid, and consequently,more useful work can be produced from the working fluid, by an expansiondevice positioned downstream of the linear constant density heatexchanger b650.

After the predetermined heating time has elapsed and the working fluidis heated at constant density to increase the temperature and pressureof the working fluid, the one or more controllers b692 can cause thefirst valve b674 and the second valve b686 to move to their respectiveopen positions such that the heated volume of working fluid flows out ofthe working chamber b654. As this occurs, a non-heated volume of workingfluid flows into the working chamber b654. That is, in causing the firstvalve b674 and the second valve b686 to move to their respective openpositions, the heated volume of working fluid flows out of the workingchamber b654 and another or second volume of working fluid is permittedto flow into the working chamber b654, e.g., to start the heating cycleonce again. The first and second valves b674, b686 can be openedsimultaneously. Alternatively, the first and second valves b674, b686can be controlled by the one or more controllers b692 to open at offsettimes.

FIG. 26 provides a schematic cross sectional view of another linearconstant density heat exchanger b650 according to an example embodimentof the present disclosure. Generally, the linear constant density heatexchanger b650 of FIG. 26 is configured in a similar manner as thelinear constant density heat exchanger b650 of FIG. 25, except asprovided below.

For this embodiment, the housing extends between a first end b660 and asecond end b662 along the axial direction A. The housing has a housinginlet port b696 at the first end b660 defining an inlet b656 of theworking chamber b654 and a housing outlet port b698 at the second endb662 defining an outlet b658 of the working chamber b654. The housinginlet port b696 of the housing is connected to (e.g., threadinglyengaged with) the inlet housing b667, which is connected to (e.g.,threadingly engaged with) the first heat exchanger port b672. An outletport b676 is disposed around the housing outlet port b698 and isconnected to (e.g., threadingly engaged with) the outlet housing b678.The housing outlet port b698 is received within the outlet port b676 asshown in FIG. 26. A sealing member b694 extends annularly around thehousing outlet port b698 and provides a seal between the housing outletport b698 and the outlet port b676. The sealing member b694 preventsheat exchange fluid HXF from exiting the outlet housing b678. The heaterhousing b688 is connected to (e.g., threadingly engaged with) the inlethousing b667 at one end and the outlet housing b678 at its other end.

Notably, for this embodiment, the housing has a plurality of heatexchange tubes b700 extending between the housing inlet port b696 andthe housing outlet port b698 of the housing. In some embodiments, theplurality of heat exchange tubes b700 include at least two (2) heatexchange tubes b700 extending between the inlet port b664 and the outletport b676. In other embodiments, the plurality of heat exchange tubesb700 include at least eight (8) heat exchange tubes b700 extendingbetween the inlet port b664 and the outlet port b676. In yet otherembodiments, the plurality of heat exchange tubes b700 include at leasttwenty (20) heat exchange tubes b700 extending between the inlet portb664 and the outlet port b676 (e.g., as shown in FIGS. 27 and 28). Insome further embodiments, the plurality of heat exchange tubes b700include at least fifty (50) heat exchange tubes b700 extending betweenthe inlet port b664 and the outlet port b676 (e.g., as shown in FIGS. 27and 28). The plurality of heat exchange tubes b700 spiral about a centeraxis (e.g., the axial centerline) defined by the housing. Further, theheat exchange tubes b700 provide fluid communication between the housinginlet port b696 and the housing outlet port b698. Accordingly, workingfluid can flow from the housing inlet port b696, through the pluralityof heat exchange tubes b700, and into the housing outlet port b698(e.g., in a left to right direction in FIG. 26). The outlet housingb678, the heater housing b688, and the inlet housing b667 define a heatexchange chamber b690, denoted as the HX chamber in FIG. 26. The heatexchange tubes b700 are received within the HX chamber. A heat exchangefluid HXF (e.g., exhaust gases from a closed cycle engine b110 disclosedherein) can flow into the linear constant density heat exchanger b650through the second heat exchanger port b684 and into the HX chamber. Theheat exchange fluid HXF can then flow in a right to left direction inFIG. 26 along the axial direction A and can impart thermal energy to theworking fluid flowing through the working chamber b654, or morespecifically, through the plurality of heat exchange tubes b700. Theheat exchange fluid HXF eventually flows into the inlet housing b667 andexits the linear constant density heat exchanger b650 through the firstheat exchanger port b672. Advantageously, the heat exchange tubes b700increase the surface area in which heat exchange fluid HXF can flowalong or against. Thus, heat transfer exchange between the heat exchangefluid HXF and the working fluid flowing through the working chamber b654(e.g., through the heat exchange tubes b700) can be made more efficientwith the spiraling heat exchange tubes b700. In some embodiments, thehousing is additively manufactured, e.g., by one or more of the methodsdescribed herein.

Referring now to FIGS. 27 and 28, FIG. 27 provides a side view of ahousing that can be implemented in a linear constant density heatexchanger b650 and FIG. 28 provides a close-up view of a second end b662of the housing of FIG. 27 and depicts a plurality of heat exchange tubesb700 with their ends cutoff for illustrative purposes. In someembodiments, for example, the housing can be implemented in the linearconstant density heat exchanger b650 of FIG. 26. As shown, the housingincludes a plurality of heat exchange tubes b700 extending between thehousing inlet port b696 and the housing outlet port b698 of the housing.The plurality of heat exchange tubes b700 spiral about a center axis(e.g., the axial centerline) defined by the housing. Specifically, theheat exchange tubes b700 are helically wound about the axial centerlineas they extend between the housing inlet port b696 and the housingoutlet port b698 of the housing. Further, for this embodiment, theplurality of tubes are arranged in radially spaced rows. Stated anotherway, the heat exchange tubes b700 are arranged in circular arrays withadjacent arrays being radially spaced from one another as viewed from anaxial cross section of the housing. In some embodiments, the circulararrays are concentrically arranged. Further, in some embodiments, theheat exchange tubes b700 are capillary or micro capillary tubes.

When the housing depicted in FIGS. 27 and 28 is implemented in a linearconstant density heat exchanger b650, the heat exchange tubes b700provide fluid communication between the housing inlet port b696 and thehousing outlet port b698. Accordingly, working fluid can flow from thehousing inlet port b696, through the plurality of heat exchange tubesb700, and into the housing outlet port b698. The outlet housing b678,the heater housing b688, and the inlet housing b667 can define a heatexchange chamber b690, e.g., as noted above. The heat exchange tubesb700 are received within the HX chamber. A heat exchange fluid HXF(e.g., exhaust gases from a closed cycle engine b110 disclosed herein)can flow into the linear constant density heat exchanger b650 throughthe second heat exchanger port b684 and into the HX chamber. The heatexchange fluid HXF can then flow along the axial direction A and canimpart thermal energy to the working fluid flowing through the workingchamber b654, or more specifically, through the plurality of heatexchange tubes b700. The heat exchange fluid HXF eventually flows intothe inlet housing b667 and exits the linear constant density heatexchanger b650 through the first heat exchanger port b672.Advantageously, the heat exchange tubes b700 increase the surface areain which heat exchange fluid HXF can flow along or against. Thus, heattransfer exchange between the heat exchange fluid HXF and the workingfluid flowing through the working chamber b654 (e.g., through the heatexchange tubes b700) can be made more efficient with the spiraling heatexchange tubes b700 arranged in radially spaced rows. In someembodiments, the housing is additively manufactured, e.g., by one ormore of the methods described herein.

FIG. 29 provides a schematic cross sectional view of another examplelinear constant density heat exchanger b650 according to an aspect ofthe present disclosure. Generally, the linear constant density heatexchanger b650 of FIG. 29 is configured in a similar manner as thelinear constant density heat exchanger b650 of FIG. 25, except asprovided below.

For this embodiment, the housing extends between a first end b660 and asecond end b662 along the axial direction A. The housing has a housinginlet port b696 at the first end b660 and a housing outlet port b698 atthe second end b662. The housing inlet port b696 defines an inlet of theworking chamber b654 and the housing outlet port b698 defines an outletof the working chamber b654. The housing has a main body b702 extendingbetween the housing inlet port b696 and the housing outlet port b698along the axial direction A. The main body b702 is generally tubular inthis example embodiment. The housing inlet port b696 of the housing isconnected to (e.g., threadingly engaged with) the inlet housing b667,which is connected to (e.g., threadingly engaged with) the first heatexchanger port b672. The outlet port b676 is disposed around the housingoutlet port b698. The outlet port b676 is connected to (e.g.,threadingly engaged with) the outlet housing b678. The housing outletport b698 is received within the outlet port b676 as shown in FIG. 29. Asealing member b694 extends annularly around the housing outlet portb698 and provides a seal between the housing outlet port b698 and theoutlet port b676. The sealing member b694 prevents heat exchange fluidHXF from exiting the outlet housing b678. The heater housing b688 isconnected to (e.g., threadingly engaged with) the inlet housing b667 atone end and the outlet housing b678 at its other end. The heater housingb688 annularly surrounds the main body b702 of the housing.

In addition, for this embodiment, the tubular housing b652 defines orhas a mesh or mesh portion b706 that extends annularly around a wallb704 of the tubular housing b652. The mesh portion b706 also extendsalong the entire main body b702 of the housing b652 along the axialdirection A. In some embodiments, the mesh portion b706 is a latticestructure. The lattice structure can be generally porous. The meshportion b706 allows for heat exchange fluid HXF to flow radially closerto the working fluid and also provides additional surface area in whichheat exchange fluid HXF can flow along or against. Thus, heat transferexchange between the heat exchange fluid HXF and the working fluidflowing through the working chamber b654 can be made more efficient withthe mesh portion b706. In some embodiments, the housing b652 isadditively manufactured, e.g., by one or more of the methods describedherein.

FIG. 30 provides a flow diagram for a method (400) of controlling alinear constant density heat exchanger b650 according to an aspect ofthe present disclosure. For instance, the method (400) can beimplemented to control any of the linear constant density heatexchangers b650 described herein. However, the scope of method (400) isnot limited to the linear constant density heat exchangers b650 providedherein. Some or all of the method (400) can be implemented by the one ormore controllers b692 and flow control devices described herein. Inaddition, it will be appreciated that exemplary method (400) can bemodified, adapted, expanded, rearranged and/or omitted in various wayswithout deviating from the scope of the present subject matter.

At (402), the method (400) includes (a) moving an inlet valve and anexit valve of the linear constant density heat exchanger b650 to an openposition such that a first volume of working fluid flows into a chamberdefined by a housing of the linear constant density heat exchanger b650.In some implementations, in moving the inlet valve and the exit valve ofthe linear constant density heat exchanger b650 to the open position at(a), a second volume of working fluid flows out of the chamber as thefirst volume of working fluid flows into the chamber. Furthermore, insome implementations, in moving the inlet valve and the exit valve ofthe linear constant density heat exchanger b650 to the open positionsuch that the first volume of working fluid flows into the chamber at(a), the inlet valve and the exit valve are moved to their respectiveopen positions simultaneously.

At (404), the method (400) includes (b) moving the inlet valve and theexit valve of the linear constant density heat exchanger b650 to aclosed position such that the first volume of working fluid is containedwithin the chamber at constant density. In some implementations, whenthe inlet valve and the exit valve of the linear constant density heatexchanger b650 are moved to their respective closed positions at (b),the second volume of working fluid is substantially removed from thechamber. Moreover, in some implementations, in moving the inlet valveand the exit valve of the linear constant density heat exchanger b650 tothe closed position such that the first volume of working fluid iscontained within the chamber at (b), the inlet valve and the exit valveare moved to the closed position simultaneously.

At (406), the method (400) includes (c) heating the first volume ofworking fluid contained within the chamber for a predetermined heatingtime while the first volume of working fluid is held at constant densitywithin the chamber. Stated another way, at (406), heat is applied to theworking fluid trapped in the working chamber b654. Accordingly, duringheat application, no additional working fluid is allowed to flow intothe working chamber b654 and working fluid is prevented from flowing outof the working chamber b654. In this way, not only is the temperature ofthe working fluid increased, the pressure of the working fluid isincreased as well. Thus, the potential energy of the working fluidheated at constant density can be increased.

At (408), the method (400) includes (d) moving the inlet valve and theexit valve of the linear constant density heat exchanger b650 to theopen position such that the heated first volume of working fluid flowsout of the chamber. In some implementations, in moving the inlet valveand the exit valve of the linear constant density heat exchanger b650 tothe open position at (d), the heated first volume of working fluid flowsout of the chamber and a third volume of working fluid flows into thechamber. Furthermore, in some implementations, in moving the inlet valveand the exit valve of the linear constant density heat exchanger b650 tothe open position such that the first volume of working fluid flows outof the chamber at (d), the inlet valve and the exit valve are moved totheir respective open positions simultaneously.

In some implementations of method (400), moving the inlet valve and theexit valve of the linear constant density heat exchanger b650 to theopen position at (a) or (402), moving the inlet valve and the exit valveof the linear constant density heat exchanger b650 to the closedposition at (b) or (404), heating the first volume of working fluidcontained within the chamber for the predetermined heating time whilethe first volume of working fluid is held at constant density within thechamber at (c) or (406), and moving the inlet valve and the exit valveof the linear constant density heat exchanger b650 to the open positionsuch that the heated first volume of working fluid flows out of thechamber at (d) or (408) defines or constitutes a heating cycle for thefirst volume of working fluid. The heating cycle can be iterated for aplurality of subsequent volumes of working fluid. Further, in someimplementations, the heating cycle is performed by the linear constantdensity heat exchanger b650 at a frequency of less than about 1.5 Hz. Insome implementations, the heating cycle is performed by the linearconstant density heat exchanger b650 at a frequency between 4 Hz and 10Hz.

In addition, in some implementations, the method (400) further includesdetermining a steady state exit mass flow rate at the outlet of thechamber for a predetermined calibration time. For instance, the steadystate exit mass flow can be determined by opening the inlet and exitvalves for a predetermined calibration time to determine the steadystate exit mass flow rate at the outlet of the chamber. For instance, asensor can be positioned at or proximate the outlet of the workingchamber b654. The sensor can be operable to sense characteristics of theworking fluid mass flow at the outlet so that the steady state exit massflow rate can be determined. In some implementations, the method (400)can further include setting a cycle time of the heating cycle based atleast in part on the determined steady state exit mass flow rate.

In some implementations, setting the cycle time of the heating cyclebased at least in part on the determined steady state exit mass flowrate includes: i) determining an average pulse exit mass flow rate atthe outlet of the chamber for a predetermined averaging time; andsetting the cycle time of the heating cycle such that the determinedsteady state exit mass flow rate and the average pulse exit mass flowrate are about equal. In yet other implementations, the method (400)includes setting a cycle time of the heating cycle about equal to a timein which a particle of the working fluid flows from the inlet to theoutlet of the linear constant density heat exchanger b650.

Rotary Constant Density Heat Exchanger

FIGS. 31 and 32 provide views of a rotary constant density heatexchanger b710 according to an example embodiment of the presentdisclosure. Particularly, FIG. 31 provides a perspective view of therotary constant density heat exchanger b710 and FIG. 32 provides a frontview thereof. Generally, like the linear constant density heatexchangers b650 described herein, the rotary constant density heatexchanger b710 is operable to hold a volume of working fluid at constantdensity during heat application. The rotary constant density heatexchanger b710 can be implemented in any of the embodiments of theNotarnicola cycle system b500 and/or any of the systems describedherein. For reference, the rotary constant density heat exchanger b710defines an axial direction A, a radial direction R, a circumferentialdirection C, and an axial centerline AC extending along the axialdirection A. The radial direction R extends to and from the axialcenterline AC in a direction orthogonal to the actual direction A. Thecircumferential direction C extends 360° around the axial centerline AC.

The rotary constant density heat exchanger b710 includes a housing b712extending between a first end b714 and a second end b716 along the axialdirection A. The housing b712 is cylindrically shaped in the depictedembodiment of FIGS. 31 and 32. However, in alternative embodiments, thehousing b712 can have another suitable shape or configuration. Thehousing b712 defines at least one working chamber b724 having an inletb726 and an outlet b728. For this embodiment, the housing b712 defines aplurality of working chambers each having an inlet b726 and an outletb728. The inlet b726 of each working chamber is defined at or proximatethe first end b714 of the housing b712 and the outlet b728 of eachworking chamber is defined at or proximate the second end b716 of thehousing b712. Each working chamber extends along the axial direction Abetween the first end b714 and the second end b716 of the housing b712.Particularly, the housing b712 has a first axial face b730 (FIG. 33) atthe first end b714 and a second axial face b732 (FIG. 33) at the secondend b716. The first axial face b730 defines the respective inlets b726of the working chambers and the second axial face b732 defines therespective outlets b728 of the working chambers. Further, the workingchambers are generally cylindrically shaped in this example embodiment,however, the working chambers can have other suitable shapes inalternative embodiments.

In addition, for this embodiment, the plurality of working chambers arearranged in a circular array along the outer periphery of thecylindrical housing b712 as shown best in FIG. 32. Specifically, theplurality of working chambers are spaced from one another along thecircumferential direction C and are arranged in the positions of thehours of a clock face. For instance, for this embodiment, the pluralityof working chambers include a first working chamber positioned at a oneo'clock position (WC-1), a second working chamber positioned at a twoo'clock position (WC-2), a third working chamber positioned at a threeo'clock position (WC-3), a fourth working chamber positioned at a fouro'clock position (WC-4), a fifth working chamber positioned at a fiveo'clock position (WC-5), a sixth working chamber positioned at a sixo'clock position (WC-6), a seventh working chamber position at a seveno'clock position (WC-7), an eighth working chamber positioned at aneight o'clock position (WC-8), a ninth working chamber positioned at anine o'clock position (WC-9), a tenth working chamber positioned at aten o'clock position (WC-10), a eleventh working chamber positioned at aeleven o'clock position (WC-11), and finally, a twelfth working chamberpositioned at a twelve o'clock or noon position (WC-12).

The rotary constant density heat exchanger b710 also includes a firstplate b718 positioned at the first end b714 of the housing b712 and asecond plate b720 positioned at the second end b716 of the housing b712.The first plate b718 is shown transparent in FIGS. 31 and 32 forillustrative purposes. The first and second plates b718, b720 arecylindrically shaped, however, the plates b718, b720 can have otherconfigurations in other example embodiments. The first plate b718 isrotatable about an axis of rotation (e.g., the axial centerline AC) suchthat the first plate b718 selectively allows working fluid to flow intoone of the working chambers. The second plate b720 is likewise rotatableabout an axis of rotation (e.g., the axial centerline AC) such that thesecond plate b720 selectively allows working fluid to flow out of one ofthe working chambers. The first plate b718 and the second plate b720 canbe rotatable about the axis of rotation in unison, for example.

The first plate b718 defines a port b722 at its outer periphery. Theport b722 defined by the first plate b718 is sized complementary toaxial cross section of one of the working chambers. When the port b722of the first plate b718 is aligned with the inlet b726 of a givenworking chamber, the first plate b718 selectively allows working fluidto flow into that working chamber. For instance, as shown in FIGS. 31and 32, the port b722 of the first plate b718 is shown aligned with theinlet b726 of the third working chamber WC-3. Accordingly, the firstplate b718 and port b722 thereof selectively allow working fluid to flowinto the third working chamber WC-3 (assuming the third working chambercan receive an additional volume of working fluid). In contrast, whenthe port b722 of the first plate b718 is not aligned with the inlet b726of a given working chamber, the first plate b718 prevents working fluidfrom flowing into that particular chamber. For instance, as illustratedin FIGS. 31 and 32, the port b722 of the first plate b718 is shownaligned with the inlet b726 of the third working chamber WC-3.Accordingly, the first plate b718 prevents working fluid from flowinginto any of the working chambers (e.g., WC-1, WC-2, WC-4, WC-5, WC-6,WC-7, WC-8, WC-9, WC-10, WC-11, and WC-12) that are not the thirdworking chamber WC-3.

The second plate b720 likewise defines a port b723, e.g., in a similarmanner as the first plate b718 defines the port b722. The port b723defined by the second plate b720 is sized complementary to axial crosssection of one of the working chambers. When the port b723 of the secondplate b720 is aligned with the outlet b728 of a given working chamber,the second plate b720 selectively allows working fluid to flow out ofthat given working chamber. For example, if the port b723 of the secondplate b720 is aligned with the outlet of the third working chamber WC-3,the second plate b720 and port b723 thereof selectively allow workingfluid to flow out of the third working chamber WC-3 (assuming the thirdworking chamber contains working fluid). In contrast, when the port b723of the second plate b720 is not aligned with the outlet of a givenworking chamber, the second plate b720 prevents working fluid fromflowing out of that particular working chamber. For example, if the portb723 of the second plate b720 is aligned with the outlet of the thirdworking chamber WC-3, the second plate b720 prevents working fluid fromflowing out of any of the working chambers that are not the thirdworking chamber WC-3.

FIGS. 33, 34, and 35 provide cross sectional views of the rotaryconstant density heat exchanger b710 of FIGS. 31 and 32. Particularly,FIG. 33 provides a cross-sectional view of the rotary constant densityheat exchanger b710 with the ports b722, b723 of the first plate b718and second plate b720 positioned at a twelve o'clock position. FIG. 34provides a cross-sectional view of the rotary constant density heatexchanger b710 with the ports b722, b723 of the first plate b718 andsecond plate b720 positioned not at the twelve o'clock position. FIG. 35provides a cross-sectional view of the rotary constant density heatexchanger b710 with the ports b722, b723 of the first plate b718 andsecond plate b720 positioned at a twelve o'clock position after onerevolution of the plates.

As depicted, a heat source b734 annularly surrounds the cylindricallyshaped housing b712. The heat source b734 is operable to impart thermalenergy to the housing b712, and in turn, the housing b712 impartsthermal energy to the working fluid contained within the workingchambers. The heat source b734 can be any suitable heat source b734,such as e.g., exhaust gases from a closed cycle engine b110 describedherein, an electric heater, etc. Further, although the heat source b734is shown positioned annularly around the cylindrical housing b712, theheat source b734 can additionally or alternatively be positionedradially inward of the plurality of working chambers, e.g., as shown inFIG. 36. Moreover, the first plate b718 and the second plate b720 can beoperatively coupled with one or more controllers b736. For instance, oneor more controllers b736 can be communicatively coupled with an electricmotor or drive mechanically coupled with the plates b718, b720, e.g.,via a shaft. The electric motor or drive can drivingly rotate the platesabout the axis of rotation. As will be explained more fully below, thefirst plate b718 and the second plate b720 are rotatable about the axisof rotation such that the heat source b734 imparts thermal energy toworking fluid held at constant density within the working chambers for apredetermined heating time.

Generally, the rotary constant density heat exchanger b710 operates in arevolver-like fashion. Particularly, the plates b718, b720 are rotatedto sequentially allow working fluid to enter/exit a given workingchamber, and while a new volume of working fluid enters a given workingchamber and a heated volume of working fluid exits that particularworking chamber, the other volumes of working fluid contained within theother working chambers are heated at constant density. Thus, as theplates b718, b720 are rotated about, a high pressure, high temperaturevolume of working fluid exits one of the working chambers, and at thesame time, a lower pressure, lower temperature volume of working fluidenters one of the working chambers. As this occurs, as noted above, heatis applied to the working fluid held at constant density within theother working chambers until released by alignment of the ports b722,b723 with the working chamber.

An example manner of operation of the rotary constant density heatexchanger b710 will now be provided. In some embodiments, the one ormore controllers b736 are configured to cause the first plate b718 andthe second plate b720 to rotate such that a first volume of the workingfluid flows into a working chamber. More specifically, the first plateb718 and the second plate b720 are rotated about the axis of rotation inunison such that the port b722 defined by the first plate b718 isaligned with the port b723 defined by the second plate b720 along thecircumferential direction C. For instance, as shown in FIG. 33, the oneor more controllers b736 can cause the first and second plates b718,b720 to rotate such that their respective ports b722, b723 arepositioned at the twelve o'clock position. When the ports b722, b723 arepositioned at the twelve o'clock position, a first volume of workingfluid V1 can flow into the twelfth working chamber WC-12 through theport of the first plate b718. In causing the first plate b718 and thesecond plate b720 to rotate such that the first volume V1 of workingfluid flows into the working chamber, a second volume of working fluidis removed from the working chamber. For instance, as the first volumeV1 of working fluid flows into the twelfth working chamber WC-12, asecond volume of fluid V1-can flow out of the twelfth working chamberWC-12 through the port of the second plate b720 as shown in FIG. 33.Thus, when the ports b722, b723 are aligned with a particular workingchamber, a new or unheated volume of working fluid flows into theworking chamber and a heated volume of working fluid flows out of theworking chamber.

After a predetermined open time, the one or more controllers b736 causethe first plate b718 and the second plate b720 to rotate such that thefirst volume of working fluid is contained or trapped within the workingchamber. In this way, the working fluid can be held at constant densityduring heat application. For instance, as shown in FIG. 34, the firstplate b718 and the second plate b720 can be rotated such that the portof the first plate b718 and the port of the second plate b720 are nolonger positioned at the twelve o'clock position. For example, if thefirst and second plates b718, b720 are rotated clockwise, the portsb722, b723 of the first and second plates b718, b720 can be positionedat the one o'clock position (or some other position that is not the 12o'clock position). If, on the other hand, the first and second platesb718, b720 are rotated counterclockwise, the ports b722, b723 of thefirst and second plates b718, b720 can be positioned at an 11 o'clockposition (or some other position that is not the 12 o'clock position).Notably, when the ports b722, b723 of the first and second plates b718,b720 are no longer positioned at the twelve o'clock position, the firstvolume V1 of working fluid is held at constant density within thetwelfth working chamber WC-12, e.g., as shown in FIG. 34. Similarly, theother volumes of working fluid held within all of the other workingchambers not in aligned with the ports b722, b723 of the first andsecond plates b718, b720, and thus, the working fluid in these workingchambers is heated at constant density as well. For instance, if thefirst and second plates b718, b720 are rotated clockwise after allowingthe first volume V1 of working fluid into the twelfth working chamberWC-12 such that the ports b722, b723 of the first and second platesb718, b720 are positioned at the one o'clock position, working fluid isheld at constant density and is heated within the second, third, fourth,fifth, sixth, seventh, eighth, ninth, tenth, eleventh, and as notedabove, the twelfth working chambers WC-2, WC-3, WC-4, WC-5, WC-6, WC-7,WC-8, WC-9, WC-10, WC-11, and WC-12.

The one or more controllers b736 are further configured to cause theheat source b734 to impart thermal energy to the first volume of workingfluid for a predetermined heating time as the first plate b718 and thesecond plate b720 hold the first volume of the working fluid at constantdensity within the working chamber. For instance, as the first volume V1is held at constant density in the twelfth working chamber WC-12 asshown in FIG. 34, the heat source b734 imparts thermal energy (e.g.,heats) to the first volume V1 of working fluid held therein as denotedby Q_(IN). The first volume V1 is heated for the predetermined heatingtime. For example, the predetermined heating time can correspond to thetime is takes the first and second plates b718, b720 to rotate onerevolution. The one or more controllers b736 can cause or continue tocause the first plate b718 and the second plate b720 to rotate such thatthe heated first volume V1 of the working fluid flows out of the twelfthworking chamber WC-12, e.g., as shown in FIG. 35. In causing the firstplate b718 and the second plate b720 to rotate such that the heatedfirst volume V1 of the working fluid flows out of the twelfth workingchamber WC-12, a third volume V1+ of working fluid is permitted to flowinto the twelfth working chamber WC-12.

As noted above, the process described above can be iterated such thatworking fluid is moved into and out of a given working chambersequentially as the first and second plates b718, b720 rotate about theaxis of rotation. Further, in some embodiments, the rotary constantdensity heat exchanger b710 is additively manufactured, e.g., by one ormore of the methods described herein.

FIG. 37 provides a front view of another rotary constant density heatexchanger b710 according to an example embodiment of the presentdisclosure. The rotary constant density heat exchanger b710 of FIG. 37is similarly configured as the rotary constant density heat exchangerb710 of FIGS. 31 through 35, expect as provided below. The housing b712(hidden in FIG. 37) of the rotary constant density heat exchanger b710can define any suitable number of working chambers. For instance, forthis embodiment, the housing b712 defines four working chambers,including a first working chamber WC-1, a second working chamber WC-2, athird working chamber WC-3, and a fourth working chamber WC-4. Asillustrated, the working chambers are spaced from one another along thecircumferential direction C and are arranged in a circular array.Notably, in this embodiment, the housing b712 defines only four workingchambers (as opposed to the twelve working chambers of the embodimentdepicted in FIGS. 31 through 35. The rotary constant density heatexchanger b710 of FIG. 37 can heat working fluid held at constantdensity for a predetermined heating time in the same or similar mannerdescribed above, except that in this embodiment, the rotating firstplate b718 and second plate b720 (hidden in FIG. 37) rotate between thefour working chambers.

FIG. 38 and FIG. 39 provide front views of another rotary constantdensity heat exchanger b710 according to an example embodiment of thepresent disclosure. The rotary constant density heat exchanger b710 ofFIGS. 38 and 39 is similarly configured as the rotary constant densityheat exchanger b710 of FIGS. 31 through 35, expect as provided below.For this embodiment, the housing b712 defines only a single workingchamber, denoted as first working chamber WC-1. As illustrated in FIG.38, the port defined by the first plate b718 is aligned with the firstworking chamber WC-1 along the circumferential direction C. The portdefined by the second plate b720 is aligned with the first workingchamber WC-1 along the circumferential direction C as well (not shown inFIG. 38). Thus, non-heated working fluid can flow into the first workingchamber WC-1 and working fluid heated at constant density can flow outof the first working chamber WC-1. Once the non-heated volume of workingfluid has moved into the first working chamber WC-1, one or morecontrollers b736 can cause the first and second plates b718, b720 torotate about the circumferential direction C to trap the working fluidin the first working chamber WC-1. As the first and second plates b718,b720 are rotated about the circumferential direction C, the heat isapplied to the working fluid held at constant density, e.g., as shown inFIG. 39. As noted previously, this can increase the temperature andpressure of the working fluid, thereby increasing the potential energyof the working fluid. After a predetermined heating time, which can besynchronized with the time associated with the plates making one or morerevolutions, the ports b722, b723 of the plates can be realigned withthe first working chamber along the circumferential direction C. In thisway, the heating cycle is completed and a new heating cycle cancommence.

FIGS. 40, 41, and 42 provide various views of another rotary constantdensity heat exchanger b710 according to an example embodiment of thepresent disclosure. For reference, the rotary constant density heatexchanger b710 defines an axial direction, a radial direction R, acircumferential direction C, and an axial centerline AC extending alongthe axial direction (into and out of the page in FIG. 40). The radialdirection R extends to and from the axial centerline AC in a directionorthogonal to the actual direction. The circumferential direction Cextends 360° around the axial centerline AC.

For this embodiment, the rotary constant density heat exchanger b710includes an annular stationary housing b740 and a rotating member b742disposed within the stationary housing b740. The rotating member b742 isrotatable about an axis of rotation, which in this embodiment is anaxial centerline, denoted as AC in FIG. 40. Thus, the rotating memberb742 is rotatable within the stationary housing b740. The rotatingmember b742 can have a cylindrical shape, for example. In someembodiments, the rotating member b742 can be rotated continuously at apredetermined rotational speed. In yet other embodiments, the rotatingmember b742 can be rotated in a non-continuous manner. The stationaryhousing b740 defines an inlet port b744 and an outlet port b746. Theinlet port b744 is spaced from the outlet port b746 along thecircumferential direction C. The inlet port b744 of the stationaryhousing b740 is operable to receive a volume of working fluid. Incontrast, the working fluid can exit the rotary constant density heatexchanger b710 via the outlet port b746. The rotating member b742, whichhas a cylindrical shape in this embodiment, defines one or more workingchambers. For this example embodiment, the rotating member b742 definesa single working chamber at an outer periphery of the rotating memberb742.

As shown in FIG. 40, when the working chamber is in communication withor aligned with the inlet port b744 of the stationary housing b740 alongthe circumferential direction C, working fluid, denoted by WF, can bemoved through the inlet port b744 and into the working chamber. As therotating member b742 is rotated about the circumferential direction C,e.g., in a counterclockwise direction (CCW), the working fluid is heldat constant density as heat is applied as denoted by Q_(IN) in FIG. 41Eventually, the working chamber becomes in communication with or alignedwith the outlet port b746 along the circumferential direction C. Asshown in FIG. 42, when the working chamber is aligned with the outletport b746 of the stationary housing b740 along the circumferentialdirection C, the working fluid WF heated at constant density can bemoved out of the working chamber and through the outlet port b746. Theapplication of heat to the working fluid held at constant densityincreases the temperature and pressure of the working fluid, whichultimately increases the potential energy of the working fluid and thusmore useful work can be produced therefrom.

To summarize, for this embodiment, the rotary constant density heatexchanger b710 has a stationary housing b740 defining an inlet port b744and an outlet port b746. The rotary constant density heat exchanger b710also has a rotating member b742 disposed within the stationary housingb740 and rotatable about an axis of rotation (e.g., the axialcenterline). The rotating member b742 defines a working chamber b748.The working chamber b748 can have any suitable shape. Notably, a volumeof working fluid is movable through the inlet port b744 and into theworking chamber b748 when the working chamber b748 is in communicationwith the inlet port b744, e.g., as depicted in FIG. 40. When the workingchamber b748 is not in communication with the inlet port b744 or theoutlet port b746 as the rotating member b742 rotates about the axis ofrotation, the volume of working fluid is held at constant density withinthe working chamber b748 and is heated by a heat source b750, e.g., asshown in FIG. 41. The volume of working fluid heated at constant densityis movable out of the working chamber b748 and through the outlet portb746 when the working chamber b748 is in communication with the outletport b746, e.g., as shown in FIG. 42.

FIG. 43 provides a schematic view of another rotary constant densityheat exchanger b710 according to an example embodiment of the presentdisclosure. The rotary constant density heat exchanger b710 of FIG. 43is similarly configured as the rotary constant density heat exchangerb710 of FIGS. 40 through 32, expect as provided below. The rotatingmember b742 of the rotary constant density heat exchanger b710 candefine any suitable number of working chambers. For instance, for thisembodiment, the rotating member b742 defines a plurality of workingchambers, including a first working chamber WC-1, a second workingchamber WC-2, a third working chamber WC-3, and a fourth working chamberWC-4. The working chambers are spaced from one another along thecircumferential direction C. Particularly, the working chambers arespaced evenly from one another along the circumferential direction C.The rotary constant density heat exchanger b710 of FIG. 43 can operatein substantially the same way as the rotary constant density heatexchanger b710 of FIGS. 40 through 32 except that heated working fluidis pulsed from the outlet port b746 of the stationary housing b740 at ahigher frequency. Moreover, having a plurality of working chambers mayallow for the rotating member b742 to rotate at a slower speed with noloss in heated working fluid output and the heat source b734 may requireless energy to heat the working fluid as the working fluid can be heatedfor a longer period of time.

Constant Density Heat Exchanger Utilizing A Positive Displacement Pump

In some example embodiments, the constant density heat exchanger caninclude a positive displacement pump. In some embodiments, for example,the constant density heat exchanger can be a positive displacementrotary pump. In other embodiments, the constant density heat exchangercan be a positive displacement reciprocating pump. Example positivedisplacement pumps include rotary lobe pumps, progressing cavity pumps,rotary gear pumps, piston pumps, diaphragm pumps, screw pumps, gearpumps, vane pumps, regenerative or peripheral pumps, and peristalticpumps.

In one example embodiment, a constant density heat exchanger includes apositive displacement rotary pump defining a chamber. The chamberreceives a working fluid and holds the working fluid at constant densitywhile a heat source b508 applies heat to the working fluid for apredetermined heating time. In some embodiments, the heat source b508 isone or more electric heating elements. For instance, the one or moreelectric heating elements can include one or more electrical resistanceheating elements. Further, in yet other embodiments, the heat sourceb508 is one or more flames.

In yet other embodiments, the heat source b508 is a cooling fluid CFhaving a temperature greater than a temperature of the working fluidheld within the chamber of the positive displacement rotary pump atconstant volume. The positive displacement rotary pump can include awall defining one or more channels. The one or more channels can receivethe cooling fluid CF. In this way, the cooling fluid CF can heat orimpart thermal energy to the working fluid held within the chamber atconstant density.

In another example embodiment, a constant density heat exchangerincludes a positive displacement reciprocating pump defining a chamber.The chamber receives a working fluid and holds the working fluid atconstant density while a heat source b508 applies heat to the workingfluid for a predetermined heating time. In some embodiments, the heatsource b508 is one or more electric heating elements. For instance, theone or more electric heating elements can include one or more electricalresistance heating elements. Further, in yet other embodiments, the heatsource b508 is one or more flames.

In yet other embodiments, the heat source b508 is a cooling fluid CFhaving a temperature greater than a temperature of the working fluidheld within the chamber of the positive displacement reciprocating pumpat constant volume. The positive displacement reciprocating pump caninclude a wall defining one or more channels. The one or more channelscan receive the cooling fluid CF. In this way, the cooling fluid CF canheat or impart thermal energy to the working fluid held within thechamber at constant density.

Wrankel Device

In some embodiments, the Notarnicola cycle systems b500 described hereincan include a Wrankel device b800. By way of example, FIG. 23 and FIG.24 provide schematic views of Notarnicola cycle systems b500 thatinclude Wrankel devices b800. Generally, a Wrankel device b800, orconstant density heat addition expansion device is operable toaccomplish two primary tasks. First, the Wrankel device b800 holds avolume of working fluid at constant density during heat application fora predetermined heating time. Second, the Wrankel device b800facilitates expansion of the high pressure, high temperature workingfluid. Energy from the expansion of the high pressure, high temperatureworking fluid can be extracted and used to produce useful work. Forinstance, the work produced can be utilized to drive a compressor and/orother accessories of one or more of the closed cycle engines describedherein.

FIGS. 44, 45, 46, and 47 provide various views of an example Wrankeldevice b800 and components thereof according to an aspect of the presentdisclosure. Particularly, FIG. 44 provides a schematic axial view of theWrankel device b800 and depicts working fluid contained at constantdensity during heat application. FIG. 45 provides a perspective view ofan example rotor b806 of the Wrankel device b800 of FIG. 44 operativelycoupled with a shaft b802 having an eccentric portion b804. FIG. 46provides an axial view of a housing b818 of the Wrankel device b800 ofFIG. 44. FIG. 47 provides another schematic axial view of the Wrankeldevice b800 of FIG. 44 and depicts heated working fluid expanding toproduce useful work.

As shown best in FIG. 44, the Wrankel device b800 includes a rotor b806having N lobes, wherein N is an integer. The rotor b806 can have anysuitable number of lobes. For this embodiment, the Wrankel device b800includes two (2) lobes, including a first lobe b808 and an opposingsecond lobe b810. The rotor b806 has a generally oval shape in thisexample embodiment, but other shapes are possible. The rotor b806 isoperatively coupled with a shaft b802 having an eccentric portion b804.Particularly, the rotor b806 is disposed on the eccentric portion b804of the shaft b802 as shown best in FIG. 45. Thus, the rotor b806 canmove in or along an eccentric motion or path. The shaft b802 can begeared to an output shaft, e.g., that can be used to drivingly rotate apump, a compressor, an electric motor, etc. In addition, the rotor b806defines an inlet port b812 operable to receive working fluid (e.g., asupercritical fluid, such as supercritical carbon dioxide) into a mainchamber b816 defined by a housing b818 of the Wrankel device b800. Therotor b806 also defines an outlet port b814 operable to receive anexpanding volume of working fluid as will be described below.

The Wrankel device b800 also includes a housing b818 defining a mainchamber b816 as noted above. As shown best in FIG. 46, the main chamberb816 defined by the housing b818 has lobe receiving regions forreceiving the lobes of the rotor b806 as the rotor b806 rotates withinthe main chamber b816, e.g., along an eccentric path. In someembodiments, the main chamber b816 defined by the housing b818 has N+1lobe receiving regions, or stated differently, the main chamber b816 hasone more lobe receiving region than the rotor b806 has lobes. As notedabove, N is an integer. For this embodiment, the main chamber b816 hasthree (3) lobe receiving regions, including a first lobe receivingregion 820, a second lobe receiving region b822, and a third lobereceiving region b824. Each of the lobe receiving regions b820, b822,b824 are sized complementary to the lobes of the rotor b806 such thatthe lobes can be received therein. For instance, as shown in FIG. 44,the first lobe b808 of the rotor b806 is received within the first lobereceiving region 820.

The housing b818 defines a plurality of constant density workingchambers. Particularly, as shown best in FIG. 46, each lobe receivingregion has an associated constant density working chamber. The firstlobe receiving region 820 has an associated first constant densityworking chamber, or first CD working chamber b826. The second lobereceiving region b822 has an associated second constant density workingchamber, or second CD working chamber b828. The third lobe receivingregion b824 has an associated third constant density working chamber, orthird CD working chamber b830. The CD working chambers b826, b828, b830are defined by the housing b818 as noted above and are positioned at theapex of each lobe receiving region. The CD working chambers b826, b828,b830 are positioned outward of the lobe receiving regions b820, b822,b824 along the radial direction R with respect to an axial centerlineAC, e.g., as shown in FIG. 46. In FIG. 46, the axial centerline extendsinto and out of the page.

During operation of the Wrankel device b800, the CD working chambersb826, b828, b830 are each operable to receive a volume of working fluidtherein. In some embodiments, the CD working chambers b826, b828, b830can receive working fluid in a sequential manner. Particularly, when agiven lobe of the rotor b806 is received within one of the lobereceiving regions b820, b822, b824, a volume of working fluid isreceived within that CD working chamber. More specifically, a volume ofworking fluid is received within that CD working chamber and held atconstant density during heat application. For instance, as shown best inFIG. 44, the first lobe b808 is received within the first lobe receivingregion 820. Accordingly, a portion of working fluid, denoted as WF inFIG. 44, that has entered the main chamber b816 via the inlet port b812becomes trapped or otherwise contained within the first CD workingchamber b826. The first lobe b808 of the rotor b806 traps the workingfluid within the first CD working chamber b826. The volume of workingfluid held within the first CD working chamber b826 can be held atconstant density for a predetermined heating time as will be explainedfurther below.

As further shown in FIG. 44, the housing b818 defines one or moreheating loops. In some embodiments, the housing b818 is additivelymanufactured. Accordingly, in such embodiments, the heating loops can beprinted or otherwise defined during the additive manufacturing process.The heating loops can be any suitable type of loop. For instance, insome embodiments, the one or more heating loops are configured toreceive a heat exchange fluid, such as e.g., hot combustion gases from aclosed cycle engine b110. In yet other embodiments, the one or moreheating loops are configured as electrical resistance wires operable toreceive an electric current therethrough, e.g., for imparting thermalenergy to surrounding structures and fluid. Accordingly, the heat sourceb832 can be a closed cycle engine b110 (e.g., such as one of the closedcycle engines described herein), an electric heating element, somecombination thereof, or some other suitable heat source b832.

The one or more heating loops b834 extend around the perimeter of thehousing b818 in this example embodiment. Notably, the one or moreheating loops b834 extend proximate each of the CD working chambersb826, b828, b830. In this way, when a volume of working fluid is held atconstant density within one of the CD working chambers b826, b828, b830,a heat exchange fluid or electric current passing through the one ormore heating loops b834 can impart thermal energy to the volume ofworking fluid. Stated another way, the one or more heating loops arepositioned at least in part in a heat exchange relationship with the CDworking chambers b826, b828, b830. Although the one or more heatingloops are shown in FIG. 44 as having only a single inlet and a singleoutlet, in other example embodiments the one or more heating loops b834can have multiple inlets and/or outlets. For instance, each CV workingchamber can have a dedicated heating loop. In this manner, the CDworking chambers b826, b828, b830 and their contents can be heated moreuniformly.

When a volume of working fluid is held at constant density within one ofthe CD working chambers b826, b828, b830, e.g., when one of the lobes ofthe rotor b806 is received within one of the lobe receiving regionsb820, b822, b824, the heat source b832 imparts thermal energy to thevolume of working fluid held at constant density for a predeterminedheating time via the heating loops b834. For instance, as shown in FIG.44, the first lobe b808 is received within the first lobe receivingregion 820, and a volume of working fluid is held at constant densitywithin the first CD working chamber b826. As the working fluid is heldat constant density, the heat source b832, or more particularly the heatexchange fluid and/or electric current flowing through the one or moreheating loops b834, imparts thermal energy to the volume of workingfluid held at constant density for a predetermined heating time. Thermalenergy or heat is shown being applied to the working fluid held atconstant density in the first CD working chamber b826, as denoted byQ_(IN). The predetermined heating time can be on the order ofmilliseconds or seconds, for example.

The application of heat to the working fluid held at constant densityincreases the temperature and pressure of the working fluid, whichultimately increases the potential energy of the working fluid. Thus,more useful work can be produced therefrom. Indeed, the temperature andpressure of the working fluid can increased such that after the heatsource b832 imparts thermal energy to the volume of working fluid heldat constant density within one of the CD working chambers b826, b828,b830 for the predetermined heating time, the now-heated volume ofworking fluid undergoes expansion. That is, the working fluid is heatedto a temperature and pressure such that the working fluid rapidlyexpands. The rapid expansion of the working fluid causes the rotor b806to rotate. The rotation or movement of the rotor b806 produces usefulwork that in turn causes the eccentric portion b804 and shaft b802 torotate. Accordingly, the shaft b802 can drive one or more components,such as e.g., a compressor of one of the closed cycle engines describedherein. As shown best in FIG. 47, the high pressure, high temperatureworking fluid heated at constant density expands outward from of thefirst CD working chamber b826, causing the rotor b806 to rotate. Thenow-expanded working fluid can exit the main chamber b816 through theoutlet port b814 of the rotor b806 and can flow downstream, e.g., to apump or cold side heat exchanger b116 of a regenerative engine. Notably,for this embodiment, the working fluid is heated at constant density toraise the temperature and pressure thereof, but the working fluid is notcombusted. Advantageously, this may allow for the working fluid to bemoved back through the Wrankel device b800, e.g., in a closed loopNotarnicola cycle system b500.

In some embodiments, as depicted in FIG. 46, the housing b818 has a peakdisposed between each pair of adjacent lobe-receiving regions. TheWrankel device b800 includes a plurality of peak seals b838. As shown,each peak b836 has an associated peak seal b838. Notably, at least oneof the plurality of peak seals b838 is configured to maintain contactwith the rotor b806 throughout a period of rotation of the rotor b806.In this way, at least one of the peak seals b838 is in contact with therotor b806 at all times. Furthermore, the peak seals b838 facilitatedirecting the working fluid from the inlet port b812 into the CD workingchambers b826, b828, b830, e.g., for heating at constant density, andfrom the CD working chambers b826, b828, b830 to the outlet port b814,e.g., after expansion.

With reference to FIGS. 48 through 53, an example manner of operation ofthe Wrankel device b800 will now be provided. FIGS. 48 through 53provide various schematic axial views of the Wrankel device b800 andshow the rotor b806 in different positions through its rotation oreccentric path. In FIGS. 48 through 53 the rotor b806 rotatescounterclockwise along an eccentric path, however, in other exampleembodiments, the rotor b806 can rotate clockwise along an eccentricpath.

As shown in FIG. 48, the first lobe b808 of the rotor b806 is receivedwithin the third lobe receiving region b824 (FIG. 46), and accordingly,some or a portion of working fluid within the main chamber b816 becomescontained within the third CD working chamber b830. As the working fluidis held at constant density within the third CD working chamber b830 bythe first lobe b808 of the rotor b806, the heat source b832 (FIG. 47)heats or imparts thermal energy to the working fluid held at constantdensity. This causes the pressure and temperature of the working fluidheld within the third CD working chamber b830 to increase.

As shown in FIG. 49, after a predetermined heating time or upon theworking fluid reaching a critical pressure within the third CD workingchamber b830, the now-heated and pressurized working fluid expands,causing the rotor b806 to move, e.g., in a counterclockwise direction.That is, the expansion of the now-heated and pressurized working fluidcauses the rotor b806 to rotate, which in turn causes the eccentricportion b804 and shaft b802 thereof to rotate, thereby producing usefulwork.

As shown in FIG. 50, the second lobe b810 of the rotor b806 is receivedwithin the second lobe receiving region b822 (FIG. 46), and accordingly,some working fluid within the main chamber b816 becomes contained ortrapped within the second CD working chamber b828 (FIG. 46). As theworking fluid is held at constant density within the second CD workingchamber b828, the heat source b832 heats or imparts thermal energy tothe working fluid held at constant density. This causes the pressure andtemperature of the working fluid held within the second CD workingchamber b828 to increase.

As shown in FIG. 51, after a predetermined heating time or upon theworking fluid reaching a critical pressure within the second CD workingchamber b828, the now-heated and pressurized working fluid expands,causing the rotor b806 to move, e.g., in a counterclockwise direction.That is, the expansion of the now-heated and pressurized working fluidcauses the rotor b806 to rotate, which in turn causes the eccentricportion b804 and shaft b802 thereof to rotate, thereby producing usefulwork.

As shown in FIG. 52, the first lobe b808 of the rotor b806 is receivedwithin the first lobe receiving region 820 (FIG. 46), and accordingly,some working fluid within the main chamber b816 becomes contained ortrapped within the first CD working chamber b826. As the working fluidis held at constant density within the first CD working chamber b826,the heat source b832 heats or imparts thermal energy to the workingfluid held at constant density. This causes the pressure and temperatureof the working fluid held within the first CD working chamber b826 toincrease.

As shown in FIG. 53, after a predetermined heating time or upon theworking fluid reaching a critical pressure within the first CD workingchamber b826, the now-heated and pressurized working fluid expands,causing the rotor b806 to move, e.g., in a counterclockwise direction.That is, the expansion of the now-heated and pressurized working fluidcauses the rotor b806 to rotate, which in turn causes the eccentricportion b804 and shaft b802 thereof to rotate, thereby producing usefulwork. After expansion, the rotor b806 can return to its position shownin FIG. 48 except that the second lobe b810 of the rotor b806 isreceived within the third lobe receiving region b824.

To summarize, as the rotor b806 rotates within the main chamber b816defined by the housing b818, the rotor b806 holds working fluid atconstant density within one of the CD working chambers b826, b828, b830during heat application. The high temperature, high pressure workingfluid then expands, driving the rotor b806 and shaft b802 operativelycoupled thereto to rotate, thereby producing useful work. The rotor b806rotates within the main chamber b816 and one of the lobes of the rotorb806 is received within a receiving lobe region in a sequential mannerthereby also utilizing the momentum of the rotor b806 to garner improvedefficiency.

FIG. 54 provides a schematic axial view of another Wrankel device b800according to an example embodiment of the present disclosure. TheWrankel device b800 of FIG. 54 is configured in a similar manner as theWrankel device b800 of FIGS. 44 through 53, except as provided below.

For this embodiment, each of the CD working chambers b826, b828, b830have an associated heat exchange loop. For instance, the first CDworking chamber b826 has an associated first heat exchange loop b840,the second CD working chamber b828 has an associated second heatexchange loop b842, and the third CD working chamber b830 has anassociated third heat exchange loop b844. The heat exchange loops b840,b842, b844 are positioned in fluid communication with their respectiveCD working chambers b826, b828, b830 and are each in thermalcommunication with a heat source b832. That is, the heat exchange loopsb840, b842, b844 are positioned at least in part in a heat exchangerelationship with a heat source b832. Each heat exchange loop can be inthermal communication with the same heat source b832, e.g., combustiongases recovered from the hot side b112 of a closed cycle engine b110, ordifferent heat sources b832. As depicted in FIG. 54, hot combustiongases can flow past or across the heat exchange loops b840, b842, b844.In this way, working fluid disposed within the heat exchange loops b840,b842, b844 can be heated by the combustion gases.

A valve b846 is positioned along each heat exchange loop b840, b842,b844. For instance, the valves b846 can be poppet valves b846. The valveb846 of each heat exchange loop b840, b842, b844 is operable toselectively allow working fluid to flow through its associated heatexchange loop b840, b842, b844. For instance, if the pressure of theworking fluid within one of the CD working chambers reaches apredetermined pressure threshold, the valve b846 can be moved to an openposition to selectively allow working fluid to flow through the heatexchange loop. On the other hand, if the pressure of the working fluidwithin the CD working chamber has not reached the predetermined pressurethreshold, the valve b846 remains in the closed position and thusprevents working fluid from flowing through the heat exchange loop.

An example manner of operation of the Wrankel device b800 of FIG. 54will now be provided. The first lobe b808 of the rotor b806 can first bereceived within the third lobe receiving region b824, and accordingly,some or a portion of working fluid within the main chamber b816 becomescontained or trapped within the third CD working chamber b830. As theworking fluid is moved into the third CD working chamber b830 by thefirst lobe b808 of the rotor b806, the pressure of the working fluidwithin the third CD working chamber b830 reaches a predeterminedpressure threshold. Accordingly, the valve b846 is moved to an openposition and consequently working fluid flows into the first heatexchange loop b840. The heat source b832 applies heat to the workingfluid held at constant density within the first heat exchange loop b840and the third CD working chamber b830. For this example, the heat sourceb832 includes combustion gases recovered from a closed cycle engineb110, such as one of the closed cycle engines described herein. Thecombustion gases impart thermal energy to the working fluid flowingthrough the first heat exchange loop b840. As the working fluid isheated at constant density, the temperature and pressure of the workingfluid increases. As the pressure of the working fluid increases, theforce the working fluid places on the first lobe b808 of the rotor b806increases as well. The force the working fluid places on the first lobeb808 of the rotor b806 eventually becomes sufficient to move the rotorb806. Particularly, the working fluid heated at constant density rapidlyexpands thereby causing the rotor b806 to move or rotate, which in turncauses the eccentric portion b804 and shaft b802 thereof to rotate,thereby producing useful work.

The rotor b806 can be moved along an eccentric path such that the secondlobe b810 of the rotor b806 is received within the second lobe receivingregion b822, and accordingly, some working fluid within the main chamberb816 becomes contained or trapped within the second CD working chamberb828. As the working fluid is moved into the second CD working chamberb828 by the second lobe b810 of the rotor b806, the pressure of theworking fluid within the second CD working chamber b828 reaches apredetermined pressure threshold. Accordingly, the valve b846 is movedto an open position and consequently working fluid flows into the secondheat exchange loop b842. The heat source b832 applies heat to theworking fluid held at constant density within the second heat exchangeloop b842 and the second CD working chamber b828. As noted above, forthis example, the heat source b832 includes combustion gases recoveredfrom a closed cycle engine b110, such as one of the closed cycle enginesdescribed herein. The combustion gases impart thermal energy to theworking fluid flowing through the second heat exchange loop b842. As theworking fluid is heated at constant density, the temperature andpressure of the working fluid increases. As the pressure of the workingfluid increases, the force the working fluid places on the second lobeb810 of the rotor b806 increases as well. The force the working fluidplaces on the second lobe b810 of the rotor b806 eventually becomessufficient to move the rotor b806. Particularly, the working fluidheated at constant density rapidly expands thereby causing the rotorb806 to move or rotate, which in turn causes the eccentric portion b804and shaft b802 thereof to rotate, thereby producing useful work.

The rotor b806 can continue to move along the eccentric path such thatthe first lobe b808 of the rotor b806 is received within the first lobereceiving region 820, and accordingly, some working fluid within themain chamber b816 becomes contained or trapped within the first CDworking chamber b826. As the working fluid is moved into the first CDworking chamber b826 by the first lobe b808 of the rotor b806, thepressure of the working fluid within the first CD working chamber b826reaches a predetermined pressure threshold. Accordingly, the valve b846is moved to an open position and consequently working fluid flows intothe first heat exchange loop b840. The heat source b832 applies heat tothe working fluid held at constant density within the first heatexchange loop b840 and the first CD working chamber b826. For thisembodiment, the heat source b832 includes combustion gases recoveredfrom a closed cycle engine b110, such as one of the closed cycle enginesdescribed herein. The combustion gases impart thermal energy to theworking fluid flowing through the first heat exchange loop b840. As theworking fluid is heated at constant density, the temperature andpressure of the working fluid increases. As the pressure of the workingfluid increases, the force the working fluid places on the first lobeb808 of the rotor b806 increases as well. The force the working fluidplaces on the first lobe b808 of the rotor b806 eventually becomessufficient to move the rotor b806. Particularly, the working fluidheated at constant density rapidly expands thereby causing the rotorb806 to move or rotate, which in turn causes the eccentric portion b804and shaft b802 thereof to rotate, thereby producing useful work. Afterexpansion, the rotor b806 can continue along its eccentric path and cancontinue along its eccentric path in the sequential manner noted above.

FIG. 55 provides an example computing system in accordance with anexample embodiment of the present disclosure. The one or morecontrollers, computing devices, or other control devices describedherein can include various components and perform various functions ofthe one or more computing devices of the computing system b2000described below.

As shown in FIG. 55, the computing system b2000 can include one or morecomputing device(s) b2002. The computing device(s) b2002 can include oneor more processor(s) b2004 and one or more memory device(s) b2006. Theone or more processor(s) b2004 can include any suitable processingdevice, such as a microprocessor, microcontroller, integrated circuit,logic device, and/or other suitable processing device. The one or morememory device(s) b2006 can include one or more computer-readable media,including, but not limited to, non-transitory computer-readable media,RAM, ROM, hard drives, flash drives, and/or other memory devices.

The one or more memory device(s) b2006 can store information accessibleby the one or more processor(s) b2004, including computer-readableinstructions b2008 that can be executed by the one or more processor(s)b2004. The instructions b2008 can be any set of instructions that whenexecuted by the one or more processor(s) b2004, cause the one or moreprocessor(s) b2004 to perform operations. In some embodiments, theinstructions b2008 can be executed by the one or more processor(s) b2004to cause the one or more processor(s) b2004 to perform operations, suchas any of the operations and functions for which the computing systemb2000 and/or the computing device(s) b2002 are configured, such as e.g.,operations for controlling certain aspects of power generation systemsand/or controlling one or more closed cycle engines as described herein.For instance, the methods described herein can be implemented in wholeor in part by the computing system b2000. Accordingly, the method can beat least partially a computer-implemented method such that at least someof the steps of the method are performed by one or more computingdevices, such as the exemplary computing device(s) b2002 of thecomputing system b2000. The instructions b2008 can be software writtenin any suitable programming language or can be implemented in hardware.Additionally, and/or alternatively, the instructions b2008 can beexecuted in logically and/or virtually separate threads on processor(s)b2004. The memory device(s) b2006 can further store data b2010 that canbe accessed by the processor(s) b2004. For example, the data b2010 caninclude models, databases, etc.

The computing device(s) b2002 can also include a network interface b2012used to communicate, for example, with the other components of system(e.g., via a network). The network interface b2012 can include anysuitable components for interfacing with one or more network(s),including for example, transmitters, receivers, ports, controllersb1510, antennas, and/or other suitable components. One or morecontrollable devices b1534 and other controllers b1510 can be configuredto receive one or more commands or data from the computing device(s)b2002 or provide one or more commands or data to the computing device(s)b2002.

The technology discussed herein makes reference to computer-basedsystems and actions taken by and information sent to and fromcomputer-based systems. One of ordinary skill in the art will recognizethat the inherent flexibility of computer-based systems allows for agreat variety of possible configurations, combinations, and divisions oftasks and functionality between and among components. For instance,processes discussed herein can be implemented using a single computingdevice or multiple computing devices working in combination. Databases,memory, instructions, and applications can be implemented on a singlesystem or distributed across multiple systems. Distributed componentscan operate sequentially or in parallel.

It should be appreciated that performances, power outputs, efficiencies,or temperature differentials at the system A10, the engine A100, orboth, provided herein may be based on a “Sea Level Static” or “StandardDay” input air condition such as defined by the United States NationalAeronautics and Space Administration, unless otherwise specified. Forexample, unless otherwise specified, conditions provided to the heaterbody, the chiller assembly, or both, or any subsystems, components, etc.therein, or any other portions of the system A10 receiving an inputfluid, such as air, are based on Standard Day conditions.

The heat transfer relationships described herein may include thermalcommunication by conduction and/or convection. A heat transferrelationship may include a thermally conductive relationship thatprovides heat transfer through conduction (e.g., heat diffusion) betweensolid bodies and/or between a solid body and a fluid. Additionally, orin the alternative, a heat transfer relationship may include a thermallyconvective relationship that provides heat transfer through convection(e.g., heat transfer by bulk fluid flow) between a fluid and a solidbody. It will be appreciated that convection generally includes acombination of a conduction (e.g., heat diffusion) and advection (e.g.,heat transfer by bulk fluid flow). As used herein, reference to athermally conductive relationship may include conduction and/orconvection; whereas reference to a thermally convective relationshipincludes at least some convection.

A thermally conductive relationship may include thermal communication byconduction between a first solid body and a second solid body, between afirst fluid and a first solid body, between the first solid body and asecond fluid, and/or between the second solid body and a second fluid.For example, such conduction may provide heat transfer from a firstfluid to a first solid body and/or from the first solid body to a secondfluid. Additionally, or in the alternative, such conduction may provideheat transfer from a first fluid to a first solid body and/or through afirst solid body (e.g., from one surface to another) and/or from thefirst solid body to a second solid body and/or through a second solidbody (e.g., from one surface to another) and/or from the second solidbody to a second fluid.

A thermally convective relationship may include thermal communication byconvection (e.g., heat transfer by bulk fluid flow) between a firstfluid and a first solid body, between the first solid body and a secondfluid, and/or between a second solid body and a second fluid. Forexample, such convection may provide heat transfer from a first fluid toa first solid body and/or from the first solid body to a second fluid.Additionally, or in the alternative, such convection may provide heattransfer from a second solid body to a second fluid.

It will be appreciated that the terms “clockwise” and“counter-clockwise” are terms of convenience and are not to be limiting.Generally, the terms “clock-wise” and “counter-clockwise” have theirordinary meaning, and unless otherwise indicated refer to a directionwith reference to a top-down or upright view. Clockwise andcounter-clockwise elements may be interchanged without departing fromthe scope of the present disclosure.

Where temperatures, pressures, loads, phases, etc. are said to besubstantially similar or uniform, it should be appreciated that it isunderstood that variations, leakages, or other minor differences ininputs or outputs may exist such that the differences may be considerednegligible by one skilled in the art. Additionally, or alternatively,where temperatures or pressures are said to be uniform, i.e., asubstantially uniform unit (e.g., a substantially uniform temperature atthe plurality of chambers A221), it should be appreciated that in oneembodiment, the substantially uniform unit is relative to an averageoperating condition, such as a phase of operation of the engine, orthermal energy flow from one fluid to another fluid, or from one surfaceto a fluid, or from one surface to another surface, or from one fluid toanother surface, etc. For example, where a substantially uniformtemperature is provided or removed to/from the plurality of chambersA221, A222, the temperature is relative to an average temperature over aphase of operation of the engine. As another example, where asubstantially uniform thermal energy unit is provided or removed to/fromthe plurality of chambers A221, A222, the uniform thermal energy unit isrelative to an average thermal energy supply from one fluid to anotherfluid relative to the structure, or plurality of structures, throughwhich thermal energy transferred.

Various interfaces, such as mating surfaces, interfaces, points,flanges, etc. at which one or more monolithic bodies, or portionsthereof, attach, couple, connect, or otherwise mate, may define orinclude seal interfaces, such as, but not limited to, labyrinth seals,grooves into which a seal is placed, crush seals, gaskets, vulcanizingsilicone, etc., or other appropriate seal or sealing substance.Additionally, or alternatively, one or more of such interfaces may becoupled together via mechanical fasteners, such as, but not limited to,nuts, bolts, screws, tie rods, clamps, etc. In still additional oralternative embodiments, one or more of such interfaces may be coupledtogether via a joining or bonding processes, such as, but not limitedto, welding, soldering, brazing, etc., or other appropriate joiningprocess.

It should be appreciated that ratios, ranges, minimums, maximums, orlimits generally, or combinations thereof, may provide structure withbenefits not previously known in the art. As such, values below certainminimums described herein, or values above certain maximums describedherein, may alter the function and/or structure of one or morecomponents, features, or elements described herein. For example, ratiosof volumes, surface area to volume, power output to volume, etc. belowthe ranges described herein may be insufficient for desired thermalenergy transfer, such as to undesirably limit power output, efficiency,or Beale number. As another example, limits greater than those describedherein may undesirably increase the size, dimensions, weight, or overallpackaging of the system or engine, such as to undesirably limit theapplications, apparatuses, vehicles, usability, utility, etc. in whichthe system or engine may be applied or operated. Still further, oralternatively, undesired increases in overall packaging may undesirablydecrease efficiency of an overall system, application, apparatus,vehicle, etc. into which the engine may be installed, utilized, orotherwise operated. For example, although an engine may be constructeddefining a similar or greater efficiency as described herein, such anengine may be of undesirable size, dimension, weight, or overallpackaging such as to reduce an efficiency of the system into which theengine is installed. As such, obviation or transgression of one or morelimits described herein, such as one or limits relative to features suchas, but not limited to, heater conduits, chiller conduits A54, chambervolumes, walled conduit volumes, or operational temperatures, orcombinations thereof, may undesirably alter such structures such as tochange the function of the system or engine.

Although specific features of various embodiments may be shown in somedrawings and not in others, this is for convenience only. In accordancewith the principles of the present disclosure, any feature of a drawingmay be referenced and/or claimed in combination with any feature of anyother drawing.

This written description uses examples to describe the presentlydisclosed subject matter, including the best mode, and also to provideany person skilled in the art to practice the subject matter, includingmaking and using any devices or systems and performing any incorporatedmethods. The patentable scope of the presently disclosed subject matteris defined by the claims, and may include other examples that occur tothose skilled in the art. Such other examples are intended to be withinthe scope of the claims if they include structural elements that do notdiffer from the literal language of the claims, or if they includeequivalent structural elements with insubstantial differences from theliteral languages of the claims. The scope of the invention(s) describedherein is defined by one or more of the claims, including combinationsof two or more claims and may include other examples that occur to thoseskilled in the art.

We claim:
 1. A constant density heat exchanger, comprising: a housingextending between a first end and a second end and defining a chamberhaving an inlet and an outlet; a first plate positioned at the first endof the housing and rotatable about an axis of rotation such that thefirst plate selectively allows a working fluid to flow into the inlet ofthe chamber; and a second plate positioned at the second end of thehousing and rotatable about the axis of rotation such that the secondplate selectively allows the working fluid to flow out of the outlet ofthe chamber, and wherein the first plate and the second plate arerotatable about the axis of rotation so as to hold a volume of theworking fluid at constant density as a heat source imparts thermalenergy thereto.
 2. The constant density heat exchanger of claim 1,wherein: the first plate defines a first port that, when aligned withthe inlet of the chamber, allows the working fluid to flow into theinlet of the chamber, and the second plate defines a second port that,when aligned with the outlet of the chamber, allows the working fluid toflow out of the outlet of the chamber.
 3. The constant density heatexchanger of claim 2, wherein the first plate and the second plate arerotatable about the axis of rotation in unison such that the first portdefined by the first plate is aligned with the second port defined bythe second plate along a circumferential direction.
 4. The constantdensity heat exchanger of claim 2, wherein the first plate and thesecond plate are rotatable about the axis of rotation so that the firstport defined by the first plate is aligned with the inlet of the chamberonly when the second port is aligned with the outlet of the chamber. 5.The constant density heat exchanger of claim 1, wherein the chamber isone of a plurality of chambers defined by the housing, each of theplurality of chambers having an inlet at the first end of the housingand an outlet at the second end of the housing.
 6. The constant densityheat exchanger of claim 5, wherein the plurality of chambers arearranged in a circular array as viewed from a perspective along an axialdirection defined by the constant density heat exchanger.
 7. Theconstant density heat exchanger of claim 6, wherein the housing iscylindrically shaped, and wherein the heat source is positioned radiallyinward of the plurality of working chambers.
 8. The constant densityheat exchanger of claim 5, wherein: the first plate defines a first portthat, when aligned with the inlet of a given one of the plurality ofchambers, allows the working fluid to flow into the inlet of the givenone of the plurality of chambers, and the second plate defines a secondport that, when aligned with the outlet of the given one of theplurality of chambers, allows the working fluid to flow out of theoutlet of the given one of the plurality of chambers, and wherein thefirst plate and the second plate are rotatable about the axis ofrotation in unison such that the first port defined by the first plateis aligned with the inlet of the given one of the plurality of chambersonly when the second port is aligned with the outlet of the given one ofthe plurality of chambers.
 9. The constant density heat exchanger ofclaim 1, wherein the housing is cylindrically shaped, and wherein theheat source annularly surrounds the cylindrically shaped housing. 10.The constant density heat exchanger of claim 1, wherein the constantdensity heat exchanger defines an axial direction, and wherein thehousing extends between the first end and the second end along the axialdirection, and wherein the chamber extends from the first end to thesecond end of the housing along the axial direction, and wherein thehousing has a first axial face at the first end and a second axial faceat the second end, and wherein the first axial face defines the inlet ofthe chamber and the second axial face defines the outlet of the chamber.11. A constant density heat exchanger, comprising: a housing extendingbetween a first end and a second end and defining a plurality ofchambers that are circumferentially arranged; a first plate positionedat the first end of the housing, the first plate defining a first port;a second plate positioned at the second end of the housing, the secondplate defining a second port aligned with the first port; and acontroller configured to: cause the first plate and the second plate torotate in unison about an axis of rotation relative to the housing sothat the first port and the second port sequentially align with theplurality of chambers one after another, and wherein, when the firstport and the second port align with a given one of the plurality ofchambers, the first port and the second port simultaneously alignrespectively with an inlet and an outlet of the given one of theplurality of chambers to allow a first volume of working fluid to enterinto the given one of the plurality of chambers through the first portand a second volume of working fluid heated at constant density to exitthe given one of the plurality of chambers through the second port. 12.The constant density heat exchanger of claim 11, wherein the controllercauses the first plate and the second plate to rotate so that the firstport and the second port align with the given one of the plurality ofchambers for a predetermined open time.
 13. The constant density heatexchanger of claim 11, wherein when the first port and the second portare aligned with the given one of the plurality of chambers, a volume ofworking fluid is held in at least one other chamber of the plurality ofchambers between the first plate and the second plate.
 14. The constantdensity heat exchanger of claim 13, wherein a heat source applies heatto the volume of working fluid held at constant density within the atleast one other chamber of the plurality of chambers.
 15. The constantdensity heat exchanger of claim 11, wherein the plurality of chambersare cylindrically shaped.
 16. A method of operating a constant densityheat exchanger, the method comprising: rotating a first plate and asecond plate about an axis of rotation relative to a housing defining aplurality of chambers that are circumferentially arranged so that afirst port defined by the first plate and a second port defined by thesecond plate sequentially align with the plurality of chambers, andwherein, when the first port and the second port align with a given oneof the plurality of chambers, the first port and the second portsimultaneously align respectively with an inlet and an outlet of thegiven one of the plurality of chambers to allow a first volume ofworking fluid to enter into the given one of the plurality of chambersthrough the first port and a second volume of working fluid heated atconstant density to exit the given one of the plurality of chambersthrough the second port.
 17. The method of claim 16, wherein when thefirst plate and the second plate are rotated in unison about the axis ofrotation.
 18. The method of claim 16, wherein the first port and thesecond port align with the given one of the plurality of chambers for apredetermined open time.
 19. The method of claim 16, wherein when thefirst port and the second port are aligned with the given one of theplurality of chambers, a volume of working fluid is held in at least oneother chamber of the plurality of chambers between the first plate andthe second plate.
 20. The method of claim 19, wherein the methodcomprises: applying heat to the volume of working fluid held at constantdensity within the at least one other chamber of the plurality ofchambers.